STOCK PURCHASE AGREEMENT BY AND BETWEEN TARGACEPT, INC. AND GLAXO GROUP LIMITED DATED AS OF JULY 27, 2007 STOCK PURCHASE AGREEMENT

Exhibit 10.2

STOCK PURCHASE AGREEMENT

BY AND BETWEEN

TARGACEPT, INC.

AND

GLAXO GROUP LIMITED

DATED AS OF JULY 27, 2007

STOCK PURCHASE AGREEMENT

THIS STOCK PURCHASE AGREEMENT (this “Agreement”) is made as of July 27, 2007, by and between Targacept, Inc., a Delaware corporation (the “Company”), and Glaxo Group Limited, a company organized under the laws of England (“GSK”).

WHEREAS the Company has agreed to sell, and GSK has agreed to purchase, the number of shares of the Company’s common stock, $0.001 par value per share (“Common Stock”), determined pursuant to Section 1.2 (the “Shares”), for an aggregate purchase price of $15,000,000 (the “Purchase Price”) in accordance with the terms and provisions hereof.

WHEREAS the Company and GSK are entering into a Product Development and Commercialization Agreement of even date herewith (the “Product Development and Commercialization Agreement”).

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereby agree as follows:

SECTION I—PURCHASE AND SALE OF SHARES

1.1. PURCHASE AND SALE OF COMMON STOCK. Subject to the terms and conditions of this Agreement and in reliance on the representations, warranties and covenants herein set forth, the Company shall issue and sell to GSK, and GSK shall purchase from the Company, the Shares for the Purchase Price.

1.2. DETERMINATION OF NUMBER OF SHARES. The number of Shares shall be equal to the quotient, rounded to the nearest whole number, obtained by dividing $15,000,000 by 125% of the average of the Daily Volume Weighted Average Prices of the Common Stock on the NASDAQ Global Market for the sixty (60)-day trading period ending two (2) trading days prior to the “Effective Date” of the Product Development and Commercialization Agreement (as defined therein). The Company represents to GSK that the spreadsheet provided to GSK by the Company on July 26, 2007 accurately sets forth the Daily Volume Weighted Average Prices for such period as listed as of such date on www.nasdaq.net.

1.3. CLOSING. Subject to the satisfaction or waiver of the conditions set forth herein, the purchase of the Shares shall be made at a closing to be held at the offices of Womble Carlyle Sandridge & Rice, PLLC, One West Fourth Street, Winston-Salem, North Carolina 27101 (by means of facsimile or overnight mail) on the date of the Product Development and Commercialization Agreement or such other date as the Company and GSK may agree, 2007 (the “Closing”).

1.4. CLOSING DELIVERY. At the Closing, subject to the terms and conditions of this Agreement: (i) GSK shall pay the Purchase Price by wire transfer of $15,000,000 in immediately available funds in accordance with the wire transfer instructions previously provided to GSK; (ii) the parties hereto shall enter into the Product Development and Commercialization Agreement; and (iii) the Company shall deliver stock certificates representing the Shares. The Shares shall be registered in the name of GSK.

EXECUTION VERSION

1.5. EXEMPTION FROM REGISTRATION. The certificate or certificates for the Shares (and any securities issued in respect of or exchange for the Shares) shall be subject to a legend or legends restricting transfer under the Securities Act of 1933, as amended (the “Securities Act”), and referring to restrictions on transfer herein, such legend to be substantially as follows:

THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE U.S. SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR APPLICABLE STATE SECURITIES LAWS AND NO INTEREST THEREIN MAY BE SOLD, TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS THERE IS AN EFFECTIVE REGISTRATION STATEMENT FOR SUCH SECURITIES UNDER THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS OR THE ISSUER OF THESE SECURITIES RECEIVES AN OPINION OF COUNSEL FOR THE HOLDER OF THESE SECURITIES SATISFACTORY TO THE ISSUER THAT REGISTRATION IS NOT REQUIRED UNDER THE ACT OR ANY APPLICABLE STATE SECURITIES LAWS.

THE TRANSFER OF THE SECURITIES REPRESENTED BY THIS CERTIFICATE IS ALSO SUBJECT TO THE RESTRICTIONS CONTAINED IN THAT CERTAIN STOCK PURCHASE AGREEMENT DATED AS OF JULY 27, 2007, BY AND BETWEEN TARGACEPT, INC. AND GLAXO GROUP LIMITED.

SECTION II—REPRESENTATIONS AND WARRANTIES OF THE COMPANY

The Company hereby represents, warrants and covenants to GSK, as of the date hereof, as follows:

2.1. ORGANIZATION AND CORPORATE POWER. The Company is duly organized and validly existing in good standing under the laws of the jurisdiction of its organization. The Company has all requisite corporate power and authority to own its properties and to carry on its business as presently conducted and as described in its Annual Report on Form 10-K for the year ended December 31, 2006. The Company is qualified to do business as a foreign corporation in each jurisdiction wherein the character of its property, or the nature of the activities presently conducted by it, makes such qualification necessary, except where the failure to be so licensed or qualified would not have a Material Adverse Effect (as defined below). “Material Adverse Effect” shall mean any events, occurrences or circumstances which give rise to or would reasonably be expected to give rise to, individually or in the aggregate, a material adverse effect on the assets, liabilities, condition (financial or other), business, results of operations of the Company.

2.2. NO SUBSIDIARIES. The Company does not currently own or control, directly or indirectly, any interest in any other corporation, partnership, trust, joint venture, limited liability company, association or other business entity.

2.3. AUTHORIZATION AND NON-CONTRAVENTION. This Agreement is a valid and binding obligation of the Company, enforceable against the Company in accordance with its terms, except as enforceability may be limited by applicable bankruptcy, insolvency, reorganization, moratorium or similar laws affecting creditors’ and contracting parties’ rights generally and except

as enforceability may be subject to general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law). The execution, delivery and performance of this Agreement, and the sale and delivery of the Shares in accordance with this Agreement, have been duly authorized by all necessary corporate or other action of the Company. The execution, delivery and performance of this Agreement, including, without limitation, the sale and delivery of the Shares in accordance with this Agreement and the performance of any transactions contemplated by this Agreement will not violate, conflict with or result in a default (whether after the giving of notice, lapse of time or both) under (i) any bond, debenture, note or any other evidence of indebtedness in any indenture, mortgage deed of trust or any other material agreement or instrument which would be reasonably likely to have a Material Adverse Effect, or to cause the creation of any lien or encumbrance upon any of the assets of the Company except for those which would not have a Material Adverse Effect, (ii) any provision of the Company’s charter or bylaws, or (iii) any provision of any law, regulation or rule, or any order of, or any restriction imposed by any court or other governmental agency applicable to the Company, except for those which would not have a Material Adverse Effect.

2.4. APPROVALS. No permit, authorization, consent, approval, or order of or by, or any, notification of or filing with, any person or entity (governmental or otherwise) is required in connection with the execution, delivery or performance of this Agreement (including the issuance and sale of the Shares) by the Company.

2.5. AUTHORIZED AND OUTSTANDING STOCK. As of March 31, 2007, the authorized capital stock of the Company consists of 100,000,000 shares of Common Stock, of which 19,142,142 shares are issued and outstanding, and 5,000,000 shares of Preferred Stock, none of which is issued and outstanding. The Company has not issued any capital stock since that date other than pursuant to (i) employee benefit plans disclosed in the SEC Documents (as defined in Section 2.6), or (ii) outstanding warrants, options or other securities disclosed in the SEC Documents. There are no preemptive rights, rights of first refusal, put or call rights or obligations or anti-dilution rights with respect to the issuance or sale of the Shares. Except as disclosed in the SEC Documents, there are no stockholders’ agreements, voting agreements or other similar agreements with respect to the Common Stock to which the Company is a party.

2.6. SEC DOCUMENTS; FINANCIAL STATEMENTS. Since December 31, 2006, the Company has filed all documents required to be filed with the United States Securities and Exchange Commission (the “SEC”) pursuant to the reporting requirements of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) (such filings since such date, the “SEC Documents”). As of their respective filing dates, each of the SEC Documents complied in all material respects with the requirements of the Exchange Act and the rules and regulations of the SEC promulgated thereunder applicable to such SEC Document, and no SEC Document when filed contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading. The financial statements of the Company and the related notes contained in the SEC Documents present fairly, in accordance with generally accepted accounting principles, the financial position of the Company as of the dates indicated, and the results of its operations and cash flows for the periods therein specified except that the unaudited interim financial statements were or are subject to normal and recurring year-end adjustments. Such financial statements (including the related notes) have been prepared in compliance in all

material respects with the published rules and regulations of the SEC and in accordance with generally accepted accounting principles applied on a consistent basis throughout the periods therein specified, except (i) as may be disclosed in the notes to such financial statements, (ii) in the case of unaudited statements, as may be permitted by the SEC on Form 10-Q under the Exchange Act and (iii) as disclosed in the SEC Documents.

2.7. NO VIOLATIONS. The Company is not: (i) in violation of its charter, bylaws, or other organizational document or any law, administrative regulation, ordinance or order of any court or governmental agency, arbitration panel or authority applicable to the Company, which violation, individually or in the aggregate, would be reasonably likely to have a Material Adverse Effect, or (ii) in default (and there exists no condition which, with the passage of time or otherwise, would constitute a default) in the performance of any bond, debenture, note or any other evidence of indebtedness in any indenture, mortgage, deed of trust or any other material agreement or instrument which is filed as an exhibit to the SEC Documents and which would be reasonably likely to have a Material Adverse Effect.

2.8. NASDAQ COMPLIANCE. The Company’s Common Stock is listed on The NASDAQ Global Market and the Company has taken no action designed to, or likely to have the effect of, de-listing the Common Stock from The NASDAQ Global Market, nor has the Company received any notification that the SEC or the National Association of Securities Dealers, Inc. (the “NASD”) is contemplating terminating such registration or listing. The Company shall comply in all material respects with all requirements of the NASD and the SEC with respect to the issuance of the Shares and the initial listing of the Shares on The NASDAQ Global Market.

2.9. COMPANY NOT AN “INVESTMENT COMPANY.” The Company has been advised generally of the rules and requirements under the Investment Company Act of 1940, as amended (the “Investment Company Act”). To the knowledge of the Company, the Company is not, and immediately after receipt of payment for the Shares will not be, an “investment company” or an entity “controlled” by an “investment company” within the meaning of the Investment Company Act.

2.10. PRIVATE OFFERING. Assuming the correctness of the representations and warranties of GSK set forth in Section 3 hereof, the offer and sale of the Shares hereunder is exempt from registration under the Securities Act.

2.11. NO BROKERS OR FINDERS. No person has or will have, as a result of the transactions contemplated by this Agreement, any right, interest or claim against or upon the Company for any commission, fee or other compensation as a finder or broker because of any act or omission by the Company or its stockholders or its affiliates.

2.12. VALID ISSUANCE OF SHARES. When issued, sold and delivered in accordance with the terms hereof for the consideration provided herein, the Shares shall be duly authorized, validly issued, fully paid and nonassessable, free from any encumbrances or restrictions on transfer other than restrictions on transfer under this Agreement and under federal and state securities laws.

SECTION III—REPRESENTATIONS AND WARRANTIES OF GSK

GSK hereby represents, warrants and covenants to the Company, as of the date hereof, as follows:

3.1. INVESTMENT REPRESENTATIONS. (i) (A) GSK is an “accredited investor” as defined in Regulation D under the Securities Act and is knowledgeable, sophisticated, able to fend for itself and experienced in making, and is qualified to make decisions with respect to investments in shares presenting an investment decision like that involved in the purchase of the Shares, including investments in securities issued by the Company and investments in comparable companies, and has requested, received, reviewed and considered all information it deemed relevant in making an informed decision to purchase the Shares and (B) the Company has made available to GSK, prior to the date hereof, the opportunity to ask questions of and receive complete and correct answers from representatives of the Company concerning the terms and conditions of the Shares and to obtain any additional information relating to the financial condition and business of the Company and GSK has such knowledge and experience in financial and business matters that GSK is capable of evaluating the merits and risks of the investment in the Shares; (ii) GSK is acquiring the Shares for its own account for investment only and with no present intention of distributing any of the Shares or any arrangement or understanding with any other persons regarding the distribution of the Shares; (iii) GSK will not, directly or indirectly, offer, sell, pledge, transfer or otherwise dispose of (or solicit any offers to buy, purchase or otherwise acquire or take a pledge of) any of the Shares except in compliance with Section 4.2 of this Agreement, the Securities Act, applicable state securities laws and the respective rules and regulations promulgated thereunder, and acknowledges that certificates evidencing the Shares will be imprinted with a legend that prohibits their transfer except in accordance therewith; and (iv) GSK has, in connection with its decision to purchase the Shares relied only upon the SEC Documents and the representations and warranties of the Company contained herein. GSK understands that its acquisition of the Shares has not been registered under the Securities Act or registered or qualified under any state securities law in reliance on specific exemptions therefrom, which exemptions may depend upon, among other things, the bona fide nature of GSK’s investment intent as expressed herein.

3.2. COMPLIANCE WITH FOREIGN SECURITIES LAWS. To the knowledge of GSK, no action is required to be taken in any jurisdiction outside the United States by the Company to permit an offering of the Shares to GSK or the possession by or distribution of offering materials to GSK in connection with the issue of the Shares. GSK will comply with all applicable laws and regulations in each foreign jurisdiction in which it purchases, offers, sells or delivers the Shares, or has in its possession or distributes any offering material, in all cases at its own expense.

3.3. AUTHORITY. (i) GSK is duly organized and validly existing under the laws of the country under which it was organized and has full corporate or other power and authority under its governing instruments and such laws to conduct its business as now conducted and to execute, deliver and perform this Agreement, (ii) GSK has full right, power, authority and capacity to enter into this Agreement and to consummate the transactions contemplated hereby and has taken all necessary action to authorize the execution, delivery and performance of this Agreement, and (iii) this Agreement constitutes a valid and binding obligation of GSK enforceable

against GSK in accordance with its terms, except as enforceability may be limited by applicable bankruptcy, insolvency, reorganization, moratorium or similar laws affecting creditors’ and contracting parties’ rights generally and except as enforceability may be subject to general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law).

3.4. INVESTMENT BANKING; BROKERAGE FEES. GSK has not incurred or taken any action so that the Company is or may become liable for any investment banking fees, brokerage commissions, broker’s or finder’s fees or similar compensation in connection with the transactions contemplated by this Agreement.

SECTION IV—COVENANTS OF THE PARTIES

4.1. RULE 144. The Company covenants that it will use commercially reasonable efforts to timely file the reports required to be filed by it under the Exchange Act and the rules and regulations adopted by the SEC thereunder (or, if the Company is not required to file such reports, it will, upon the request of GSK (or any of its affiliates which then holds any of the Shares) made after the first anniversary of the Closing, make publicly available such information as necessary to permit sales pursuant to Rule 144 under the Securities Act), and it will take such further action as GSK may reasonably request, all to the extent required from time to time to enable GSK, whichever then holds any of the Shares, to sell such Shares without registration under the Securities Act but within the limitations of Rule 144 under the Securities Act, as such Rule may be amended from time to time, or any successor rule or regulation hereafter adopted by the SEC (but subject, in any case, to applicable insider trading laws). Upon the reasonable request of GSK, the Company will deliver to such holder a written statement as to whether it has complied with such and requirements.

4.2. SELLING RESTRICTIONS.

A. Except as set forth in this Section 4.2(A), GSK agrees that it shall not sell, transfer, pledge, hypothecate or otherwise dispose of (each a “Transfer”) any of the Shares purchased at the Closing prior to the first anniversary of the Closing and, thereafter only in compliance with Rule 144 or other applicable exemption from registration under the Securities Act. The restriction on Transfer set forth in this Section 4.2 shall not apply to Transfers to a subsidiary or parent of GSK or to “affiliates” (as defined in Rule 405 of the Securities Act) or stockholders of GSK, provided that each transferee agrees in writing as a condition precedent to such Transfer to be bound by the terms of this Agreement. For as long as GSK and its affiliates together own more than five percent (5%) of the outstanding shares of Common Stock, GSK shall give the Company written notice of any intended Transfer of any of the Shares not later than the time of such Transfer. GSK also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar to restrict the transfer of the Shares except in compliance with this Section 4.2.

B. GSK agrees that it shall not, and it shall cause its affiliates not to, directly or indirectly, sell any shares of Common Stock that it (or its affiliate) does not “own” (within the meaning of Rule 200(b) and (c) of Regulation SHO promulgated by the SEC under the Exchange Act). Without limiting the generality of the foregoing, GSK shall not, and shall cause its affiliates not

to, (i) enter into a short position with respect to any shares of Common Stock, (ii) grant any option to purchase or acquire any right to dispose or otherwise dispose for value of any shares of Common Stock or any securities convertible into, exercisable for or exchangeable for any shares of Common Stock, or (iii) enter into any swap, hedge or other agreement that transfers, in whole or in part, the economic risk of ownership of any shares of Common Stock.

4.3. CONFIDENTIALITY; NON-DISCLOSURE. Each party represents to the other that, at all times during the Company’s offering of the Shares to GSK, it has maintained in confidence all non-public information regarding the other, and covenants that it will continue to maintain in confidence such information until such information pursuant to Article 9 of the Product Development and Commercialization Agreement, except as follows: (i) at Closing, the Company may issue a press release disclosing information regarding its transaction with GSK that the Company believes constitutes material and non-public information and (ii) the Company shall, within four (4) business days of the Closing, file with the SEC a report on Form 8-K disclosing the material terms of the transactions contemplated hereby and by the Product Development and Commercialization Agreement. For the avoidance of doubt, the parties agree that the information to be disclosed by the Company hereunder shall be deemed authorized disclosure under Section 9.2 of the Product Development and Commercialization Agreement.

SECTION V—MISCELLANEOUS

5.1. SURVIVAL OF REPRESENTATIONS AND WARRANTIES. The representations and warranties of the Company and GSK contained herein shall survive the execution of this Agreement, the delivery to GSK of the Shares being purchased and the payment therefor until 12 months from and after the date hereof.

5.2. AMENDMENTS, WAIVERS AND CONSENTS. For the purposes of this Agreement, except as otherwise specifically set forth herein, no course of dealing between the Company on the one hand and GSK on the other and no delay on the part of any party hereto in exercising any rights hereunder or thereunder shall operate as a waiver of the rights hereof and thereof. Any term or provision hereof may be amended, terminated or waived (either generally or in a particular instance and either retroactively or prospectively) only with the written consent of the Company and GSK.

5.3. NOTICES AND DEMANDS. All notices, requests, demands and other communications hereunder shall be in writing and shall be deemed to have been duly given if faxed (with transmission acknowledgment received), delivered personally or mailed by certified or registered mail (return receipt requested) as follows:

or to such other address or fax number of which any party may notify the other parties as provided above. Notices shall be effective as of the date of such delivery, mailing or fax.

5.4. SEVERABILITY. Whenever possible, each provision of this Agreement shall be interpreted in such a manner as to be effective and valid under applicable law, but if any provision of this Agreement shall be deemed prohibited or invalid under such applicable law, such provision shall be ineffective to the extent of such prohibition or invalidity, and such prohibition or invalidity shall not invalidate the remainder of such provision or the other provisions of this Agreement.

5.5. EXPENSES. Each of the parties shall be responsible for its own costs and expenses incurred in connection with the transactions contemplated hereby and all agreements, documents and instruments executed pursuant hereto.

5.6. COUNTERPARTS. This Agreement may be executed in multiple counterparts, each of which shall constitute an original but all of which shall constitute but one and the same instrument. One or more counterparts of this Agreement may be delivered via telecopier, with the intention that they shall have the same effect as an original counterpart hereof.

5.7. EFFECT OF HEADINGS; CONSTRUCTION. The descriptive headings in this Agreement have been inserted for convenience only and shall not be deemed to limit or otherwise affect the construction of any provision thereof or hereof. The parties have participated jointly in the negotiation and drafting of this Agreement with counsel sophisticated in investment transactions. In the event an ambiguity or question of intent or interpretation arises, this Agreement and the agreements, documents and instruments executed and delivered in connection herewith shall be construed as if drafted jointly by the parties and no presumption or burden of proof shall arise favoring or disfavoring any party by virtue of the authorship of any provisions of this Agreement and the agreements, documents and instruments executed and delivered in connection herewith.

5.8. GOVERNING LAW. This Agreement shall be deemed a contract made under the laws of North Carolina and all disputes, claims or controversies arising out of this Agreement, or the negotiation, validity or performance hereof or the transactions contemplated herein, shall be construed under and governed by the laws of such state, without giving effect to its conflicts of laws principles.

5.9. ENTIRE AGREEMENT. This Agreement (and the provisions of the Product Development and Commercialization Agreement specifically referenced herein) constitutes the full and entire understanding and agreement among the parties hereto with respect to the subject matters hereof and thereof, and any and all other written or oral agreements existing prior to or contemporaneously herewith are expressly superseded and canceled.

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IN WITNESS WHEREOF, the undersigned have executed this Stock Purchase Agreement as of the day and year first above written.