CHESAPEAKE ENERGY CORPORATION 2002 NONQUALIFIED STOCK OPTION PLAN

Exhibit 10.1.13

CHESAPEAKE ENERGY CORPORATION

2002 NONQUALIFIED STOCK OPTION PLAN

(as amended through June 6, 2008)

CHESAPEAKE ENERGY CORPORATION

2002 NONQUALIFIED STOCK OPTION PLAN

Table of Contents

ARTICLE I

PURPOSE

Section 1.1 Purpose. This Stock Option Plan is established by Chesapeake Energy Corporation (the “Company”) to create incentives which are designed to motivate Employees and Consultants to put forth maximum effort toward the success and growth of the Company and to enable the Company to attract and retain experienced individuals who by their position, ability and diligence are able to make important contributions to the Company’s success. Toward these objectives, the Plan provides for the granting of Options to Employees and Consultants on the terms and subject to the conditions set forth in the Plan.

Section 1.2 Establishment. The Plan is effective as of March 1, 2002 and for a period of 10 years from such date. The Plan will terminate on February 29, 2012; however, it will continue in effect until all matters relating to the exercise of Options and administration of the Plan have been settled.

Section 1.3 Shares Subject to the Plan. Subject to Articles IV, VII and IX of this Plan, shares of stock covered by Options shall consist of Four Million (4,000,000) shares of Common Stock.

ARTICLE II

DEFINITIONS

Section 2.1 “Board” means the Board of Directors of the Company.

Section 2.2 “Code” means the Internal Revenue Code of 1986, as amended. Reference in the Plan to any Section of the Code shall be deemed to include any amendments or successor provisions to such Section and any regulations under such Section.

Section 2.3 “Committee” has the meaning set forth in Section 3.1.

Section 2.4 “Common Stock” means the common stock, par value $.01 per share, of the Company and, after substitution, such other stock as shall be substituted therefor as provided in Article VII or Article IX of the Plan.

Section 2.5 “Consultant” means any person who is engaged by the Company, a subsidiary or a partnership or limited liability company which the Company controls to render consulting or advisory services.

Section 2.6 “Date of Grant” means the date on which the granting of an Option is authorized by the Committee or such later date as may be specified by the Committee in such authorization.

Section 2.7 “Disability” has the meaning set forth in Section 22(e)(3) of the Code.

Section 2.8 “Eligible Person” means any Employee or Consultant.

Section 2.9 “Employee” means any employee of the Company, a Subsidiary or a partnership or limited liability company which the Company controls.

Section 2.10 “Exchange Act” means the Securities Exchange Act of 1934, as amended.

Section 2.11 “Executive Officer Participants” means Participants who are subject to the provisions of Section 16 of the Exchange Act with respect to the Common Stock.

Section 2.12 “Fair Market Value” means, as of any date, (i) if the principal market for the Common Stock is a national securities exchange or the Nasdaq stock market, the closing price of the Common Stock on that date on the principal exchange on which the Common Stock is then listed or admitted to trading; or (ii) if sale prices are not available or if the principal market for the Common Stock is not a national securities exchange and the Common Stock is not quoted on the Nasdaq stock market, the average of the highest bid and lowest asked prices for the Common Stock

on such day as reported on the Nasdaq OTC Bulletin Board Service or by the National Quotation Bureau, Incorporated or a comparable service. If the day is not a business day, and as a result, clauses (i) and (ii) are inapplicable, the Fair Market Value of the Common Stock shall be determined as of the last preceding business day. If clauses (i) and (ii) are otherwise inapplicable, the Fair Market Value of the Common Stock shall be determined in good faith by the Committee.

Section 2.13 “Non-Executive Officer Participants” means Participants who are not subject to the provisions of Section 16 of the Exchange Act.

Section 2.14 “Nonqualified Stock Option” means an option to purchase shares of Common Stock which is not an incentive stock option within the meaning of Section 422(b) of the Code.

Section 2.15 “Option” means a Nonqualified Stock Option granted under Article VI of the Plan.

Section 2.16 “Option Agreement” means any written instrument that establishes the terms, conditions, restrictions, and/or limitations applicable to an Option in addition to those established by this Plan and by the Committee’s exercise of its administrative powers.

Section 2.17 “Participant” means an Eligible Person to whom an Option has been granted by the Committee under the Plan.

Section 2.18 “Plan” means the Chesapeake Energy Corporation 2002 Nonqualified Stock Option Plan.

Section 2.19 “Regular Stock Option Committee” means the Employee Compensation and Benefits Committee designated by the Board which shall consist of not less than one member of the Board.

Section 2.20 “Special Stock Option Committee” means a committee designated by the Board which shall consist of not less than two members of the Board who meet the definition of “non-employee directors” pursuant to Rule 16b-3, or any successor rule, promulgated under Section 16 of the Exchange Act.

Section 2.21 “Subsidiary” shall have the same meaning set forth in Section 424 of the Code.

ARTICLE III

ADMINISTRATION

Section 3.1 Administration of the Plan; the Committee. The Regular Stock Option Committee shall administer the Plan with respect to Non-Executive Officer Participants, including the grant of Options, and the Special Stock Option Committee shall administer the Plan with respect to Executive Officer Participants, including the grant of Options. Accordingly, as used in the Plan, the term “Committee” shall mean the Regular Stock Option Committee if it refers to Plan administration affecting Non-Executive Officer Participants or the Special Stock Option Committee if it refers to Plan administration affecting Executive Officer Participants. If in either case the Committee does not exist, or for any other reason determined by the Board, the Board may take any action under the Plan that would otherwise be the responsibility of the Committee.

Unless otherwise provided in the by-laws of the Company or resolutions adopted from time to time by the Board establishing the Committee, the Board may from time to time remove members from, or add members to, the Committee. Vacancies on the Committee, however caused, shall be filled by the Board. The Committee shall hold meetings at such times and places as it may determine. A majority of the Committee shall constitute a quorum, and the acts of a majority of the members present at any meeting at which a quorum is present shall be the valid acts of the Committee. Any action which may be taken at a meeting of the Committee may be taken without a meeting if all the members of the Committee consent to the action in writing.

Subject to the provisions of the Plan, the Committee shall have exclusive power to:

(a) Select the Eligible Persons to participate in the Plan.

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(b) Determine the time or times when Options will be granted.

(c) Determine the number of shares of Common Stock subject to any Option, all the terms, conditions (including performance requirements), restrictions and/or limitations, if any, of an Option, including the time and conditions of exercise or vesting, and the terms of any Option Agreement, which may include the waiver or amendment of prior terms and conditions or acceleration of the vesting or exercise of an Option under certain circumstances determined by the Committee.

(d) Determine whether Options will be granted singly or in combination.

(e) Take any and all other action it deems necessary or advisable for the proper operation or administration of the Plan.

Section 3.2 Committee to Make Rules and Interpret Plan. The Committee in its sole discretion shall have the authority, subject to the provisions of the Plan, to establish, adopt, or revise such rules and regulations and to make all such determinations relating to the Plan as it may deem necessary or advisable for the administration of the Plan. The Committee’s interpretation of the Plan or any Options granted pursuant hereto and all decisions and determinations by the Committee with respect to the Plan shall be final, binding, and conclusive on all parties.

ARTICLE IV

GRANT OF OPTIONS

The Committee may, from time to time, grant Options to one or more Participants, provided, however, that:

(a) At least a majority of the shares of Common Stock underlying Options granted under the Plan during any three-year period must be granted to employees who are not Executive Officer Participants or directors of the Company.

(b) Any shares of Common Stock related to Options which terminate by expiration, forfeiture, cancellation or otherwise without the issuance of shares of Common Stock shall be available again for grant under the Plan.

(c) Common Stock delivered by the Company upon exercise of an Option under the Plan will be authorized and unissued shares or issued shares which have been reacquired by the Company (i.e., treasury shares).

(d) The Committee shall, in its sole discretion, determine the manner in which fractional shares arising under this Plan shall be treated.

(e) Upon the exercise of any Option, the Company shall issue and deliver to the Participant who exercised the Option a certificate representing the number of shares of Common Stock purchased thereby.

ARTICLE V

ELIGIBILITY

Subject to the provisions of the Plan, the Committee shall, from time to time, select from the Eligible Persons those to whom Options shall be granted and shall establish in the related Option Agreements the terms, conditions, restrictions and/or limitations, if any, applicable to the Options in addition to those set forth in the Plan and the administrative rules and regulations issued by the Committee.

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ARTICLE VI

STOCK OPTIONS

Section 6.1 Grant of Options. The Committee may, from time to time, subject to the provisions of the Plan and such other terms and conditions as it may determine, grant Nonqualified Stock Options to Eligible Persons. Each grant of an Option shall be evidenced by an Option Agreement executed by the Company and the Participant, and shall contain such terms and conditions and be in such form as the Committee may from time to time approve, subject to the requirements of Section 6.2.

Section 6.2 Conditions of Options. Each Option so granted shall be subject to the following conditions:

(a) Exercise Price. The Option Agreement for each Option shall state the exercise price which shall be set by the Committee on the Date of Grant. No Option shall be granted at an exercise price which is less than the Fair Market Value of the Common Stock on the Date of Grant, except that Options for the purchase of up to ten percent (10%) of the shares subject to the Plan may be granted at an exercise price which is not less than eighty-five percent (85%) of the Fair Market Value of the Common Stock on the Date of Grant.

(b) Form of Payment. The payment of the exercise price of an Option shall be subject to the following:

(c) Exercise of Options. Options granted under the Plan shall be exercisable, in whole or in such installments and at such times, and shall expire at such time, as shall be provided by the Committee in the Option Agreement. Exercise of an Option shall be by written notice stating the election to exercise in the form and manner determined by the Committee. Every share of Common Stock acquired through the exercise of an Option shall be deemed to be fully paid at the time of exercise and payment of the exercise price.

(d) Other Terms and Conditions. Among other conditions that may be imposed by the Committee, if deemed appropriate, are those relating to (i) the period or periods and the conditions of exercisability of any Option; (ii) the minimum periods during which Participants must be employed by the Company or its Subsidiaries, or must hold Options before they may be exercised; (iii) the minimum periods during which shares acquired upon exercise must be held before sale or transfer shall be permitted; (iv) the

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maximum period that Participants will be allowed to be inactively employed or on a leave of absence before their vesting is suspended until they return to active employment; (v) conditions under which such Options or shares may be subject to forfeiture; (vi) the frequency of exercise or the minimum or maximum number of shares that may be acquired at any one time and (vii) the achievement by the Company of specified performance criteria.

(e) Application of Funds. The proceeds received by the Company from the sale of Common Stock issued upon the exercise of Options will be used for general corporate purposes.

(f) Shareholder Rights. No Participant shall have any rights as a shareholder with respect to any share of Common Stock subject to an Option prior to the purchase of such share of Common Stock by exercise of the Option.

ARTICLE VII

STOCK ADJUSTMENTS

Subject to the provisions of Article IX of this Plan, in the event that the shares of Common Stock, as presently constituted, shall be changed into or exchanged for a different number or kind or shares of stock or other securities of the Company or of another corporation (whether by reason of merger, consolidation, recapitalization, reclassification, stock split, combination of shares or otherwise), or if the number of such shares of Common Stock shall be increased through the payment of a stock dividend, or a dividend on the shares of Common Stock or rights or warrants to purchase securities of the Company shall be made, then there shall be substituted for or added to each share available under and subject to the Plan as provided in Section 1.3 hereof, and each share then subject or thereafter subject or which may become subject to Options under the Plan, the number and kind of shares of stock or other securities into which each outstanding share of Common Stock shall be so changed or for which each such share shall be exchanged or to which each such share shall be entitled, as the case may be, on a fair and equivalent basis in accordance with the applicable provisions of Section 424 of the Code; provided, however, in no such event will such adjustment result in a modification of any Option as defined in Section 424(h) of the Code. In the event there shall be any other change in the number or kind of the outstanding shares of Common Stock, or any stock or other securities into which the Common Stock shall have been changed or for which it shall have been exchanged, then if the Committee shall, in its sole discretion, determine that such change equitably requires an adjustment in the shares available under and subject to the Plan, or in any Option theretofore granted or which may be granted under the Plan, such adjustments shall be made in accordance with such determination, except that no adjustment of the number of shares of Common Stock available under the Plan or to which any Option relates that would otherwise be required shall be made unless and until such adjustment either by itself or with other adjustments not previously made would require an increase or decrease of at least 1% of the number of shares of Common Stock available under the Plan or to which any Option relates immediately prior to the making of such adjustment (the “Minimum Adjustment”). Any adjustment representing a change of less than such minimum amount shall be carried forward and made as soon as such adjustment together with other adjustments required by this Article VII and not previously made would result in a Minimum Adjustment. Notwithstanding the foregoing, any adjustment required by this Article VII which otherwise would not result in a Minimum Adjustment shall be made with respect to shares of Common Stock relating to any Option immediately prior to exercise of such Option.

No fractional shares of Common Stock or units of other securities shall be issued pursuant to any such adjustment, and any fractions resulting from any such adjustment shall be eliminated in each case by rounding downward to the nearest whole share.

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ARTICLE VIII

GENERAL

Section 8.1 Amendment or Termination of Plan. The Board may suspend or terminate the Plan at any time. In addition, the Board may, from time to time, amend the Plan in any manner in accordance with applicable federal or state laws or regulations.

Section 8.2 Acceleration of Otherwise Unexercisable Stock Options on Death, Disability or Other Special Circumstances. The Committee, in its sole discretion, may permit (i) a Participant who terminates employment due to a Disability, (ii) the personal representative of a deceased Participant, or (iii) any other Participant who terminates employment upon the occurrence of special circumstances (as determined by the Committee) to purchase all or any part of the shares subject to any unvested Option on the date of the Participant’s termination of employment due to a Disability, death or special circumstances, or as the Committee otherwise so determines. With respect to Options which have already vested at the date of such termination or the vesting of which is accelerated by the Committee in accordance with the foregoing provision, the Participant or the personal representative of a deceased Participant shall have the right to exercise such vested Options within such period(s) as the Committee shall determine.

Section 8.3 Nonassignability. Options are not transferable otherwise than by will or the laws of descent and distribution. Any attempted transfer, assignment, pledge, hypothecation or other disposition of, or the levy of execution, attachment or similar process upon, any Option contrary to the provisions hereof shall be void and ineffective, shall give no right to any purported transferee, and may, at the sole discretion of the Committee, result in forfeiture of the Option involved in such attempt.

Section 8.4 Withholding Taxes. A Participant must pay to the Company the amount of taxes required by law upon the exercise of an Option in cash, unless an alternative payment method is acceptable by the Committee.

Section 8.5 Regulatory Approval and Listings. The Company shall use its best efforts to file with the Securities and Exchange Commission as soon as practicable following the date this Plan is effective, and keep continuously effective and usable, a Registration Statement on Form S-8 with respect to shares of Common Stock subject to Options hereunder. Notwithstanding anything contained in this Plan to the contrary, the Company shall have no obligation to issue or deliver certificates representing shares of Common Stock evidencing Options prior to:

(a) the obtaining of any approval from, or satisfaction of any waiting period or other condition imposed by, any governmental agency which the Committee shall, in its sole discretion, determine to be necessary or advisable;

(b) the listing of such shares on any exchange on which the Common Stock may be listed; and

(c) the completion of any registration or other qualification of such shares under any state or federal law or regulation of any governmental body which the Committee shall, in its sole discretion, determine to be necessary or advisable.

Section 8.6 Right to Continued Employment. Participation in the Plan shall not give any Participant any right to remain in the employ of the Company or any Subsidiary or any partnership or limited liability company controlled by the Company. Further, the adoption of this Plan shall not be deemed to give any Employee or Consultant or any other individual any right to be selected as a Participant or to be granted an Option.

Section 8.7 Reliance on Reports. Each member of the Committee and each member of the Board shall be fully justified in relying or acting in good faith upon any report made by the independent public accountants of the Company and its Subsidiaries and upon any other information furnished in connection with the Plan by any person or persons other than the Committee or Board member. In no event shall any person who is or shall have been a member of the Committee or of the Board be liable for any determination made or other action taken or any omission to act in reliance upon any such report or information or for any action taken, including the furnishing of information, or failure to act, if in good faith.

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Section 8.8 Construction. The titles and headings of the sections in the Plan are for the convenience of reference only, and in the event of any conflict, the text of the Plan, rather than such titles or headings, shall control.

Section 8.9 Governing Law. The Plan shall be governed by and construed in accordance with the laws of the State of Oklahoma except as superseded by applicable federal law.

ARTICLE IX

ACCELERATION OF OPTIONS UPON CORPORATE EVENT

Section 9.1 Procedures for Acceleration and Exercise. If the Company shall, pursuant to action by the Board, at any time propose to dissolve or liquidate or merge into, consolidate with, or sell or otherwise transfer all or substantially all of its assets to another corporation and provision is not made pursuant to the terms of such transaction for the assumption by the surviving, resulting or acquiring corporation of outstanding Options under the Plan, or for the substitution of new options therefor, the Committee shall cause written notice of the proposed transaction to be given to each Participant no less than forty days prior to the anticipated effective date of the proposed transaction, and the Participant’s Option shall become 100% vested. Prior to a date specified in such notice, which shall be not more than ten days prior to the anticipated effective date of the proposed transaction, each Participant shall have the right to exercise his or her Option to purchase any or all of the Common Stock then subject to such Option. Each Participant, by so notifying the Company in writing, may, in exercising his or her Option, condition such exercise upon, and provide that such exercise shall become effective immediately prior to the consummation of the transaction, in which event such Participant need not make payment for the Common Stock to be purchased upon exercise of such Option until five days after receipt of written notice by the Company to such Participant that the transaction has been consummated. If the transaction is consummated, each Option, to the extent not previously exercised prior to the date specified in the foregoing notice, shall terminate on the effective date such transaction is consummated. If the transaction is abandoned, (i) any Common Stock not purchased upon exercise of such Option shall continue to be available for purchase in accordance with the other provisions of the Plan and (ii) to the extent that any Option not exercised prior to such abandonment shall have vested solely by operation of this Section 9.1, such vesting shall be deemed voided as of the time such acceleration otherwise occurred pursuant to Section 9.1, and the vesting schedule set forth in the Participant’s Option Agreement shall be reinstituted as of the date of such abandonment.

Section 9.2 Certain Additional Payments by the Company. The Committee may, in its sole discretion, provide in any Option Agreement for certain payments by the Company in the event that acceleration of vesting of any Option under the Plan is subject to the excise tax imposed by Section 4999 of the Code or any interest or penalties with respect to such excise tax (such excise tax, interest and penalties, collectively, the “Excise Tax”). An Option Agreement may provide that the Participant shall be entitled to receive a payment (a “Gross-Up Payment”) in an amount such that after payment by the Participant of all taxes (including any interest or penalties imposed with respect to such taxes), including any Excise Tax, imposed upon the Gross-Up Payment, the Participant retains an amount of the Gross-Up Payment equal to the Excise Tax imposed upon such acceleration of vesting of any Option.

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