ALEXION PHARMACEUTICALS, INC. 2004 INCENTIVE PLAN

Exhibit 10.27

ALEXION PHARMACEUTICALS, INC.

2004 INCENTIVE PLAN

RESTRICTED STOCK AWARD AGREEMENT

THIS AGREEMENT, made as of this              day of                 , 200     (the “Grant Date”), by and between Alexion Pharmaceuticals, Inc., a Delaware corporation (the “Company”), and you (“Participant”) sets forth the terms and conditions of an Award of Restricted Stock granted to Participant under the Alexion Pharmaceuticals, Inc. 2004 Incentive Plan (the “Plan”).

W I T N E S S E T H:

Pursuant to the Plan, the Company desires to grant Participant, and Participant desires to accept, an Award of Restricted Stock, upon the terms and conditions set forth in this Agreement and the Plan. Capitalized terms used but not defined herein shall have the meanings ascribed to such terms in the Plan.

NOW, THEREFORE, the parties hereto agree as follows:

1. Grant. The Company hereby grants to Participant the number of shares of Stock (the “Shares”) set forth in an award letter delivered to Participant together with this Agreement (the “Award Letter”), subject to the terms and conditions of the Plan and this Agreement. The Shares are subject to certain transfer and forfeiture restrictions pursuant to this Agreement, which shall expire, if at all, in accordance with Section 2 below. While such restrictions are in effect, the Shares subject to such restrictions shall be referred to as “Restricted Stock.”

2. Vesting. Except as otherwise provided in an employment or other agreement between Participant and the Company or its affiliates, the Restricted Stock shall become vested, and cease to be Restricted Stock, in the amounts and on the dates specified in the Award Letter (each, a “Vesting Date”), provided that Participant remains in the continuous employment or other service of the Company or its affiliates through each applicable Vesting Date.

3. Restrictions on Transfer. Shares of Restricted Stock shall not be sold, assigned, transferred, disposed of, pledged or otherwise hypothecated by Participant (other than to the Company) unless and until they become vested and cease to be Restricted Stock pursuant to Section 2 above. Any attempted sale, assignment, transfer, disposition, pledge or hypothecation of shares of Restricted Stock in violation of this Agreement shall be void and of no effect and the Company shall have the right to disregard the same on its books and records and issue “stop transfer” instructions to its transfer agent.

4. Forfeiture. Except as otherwise provided in an employment or other agreement between Participant and the Company or its affiliates or in the Plan, Participant shall immediately forfeit to the Company any and all Restricted Stock, and all rights and interests therein, without compensation, upon the cessation of Participant’s employment or other service with the Company or its affiliates.

5. Stock Certificates. The Restricted Stock shall be evidenced by book entries on the Company’s stock transfer records pending the expiration of restrictions thereon or shall be evidenced by certificates, which shall be retained in the physical possession of the Company until the Shares become vested. Participant shall deliver to the Company the stock power and assignment, in the form of Exhibit A attached to this Agreement, endorsed in blank, relating to the Restricted Stock as soon as practical after the Grant Date. It is a condition to your receipt of the Restricted Stock that you complete and return the stock power to the Company within 30 days of receipt of this Agreement. If you fail to complete and return the stock power in such time period, the Company may revoke this grant and your Restricted Stock will be deemed forfeited.

6. Voting and Dividends. Participant shall be entitled to exercise voting rights with respect to the Restricted Stock notwithstanding the restrictions imposed on the Restricted Stock herein. Any cash or stock dividends paid on the Restricted Stock shall be remitted to Participant, subject to applicable withholding. Any cash, property or other securities distributed in respect of or exchanged for the Restricted Stock shall be subject to the restrictions and risk of forfeiture to the same extent as the Restricted Stock, or as otherwise determined by the Committee.

7. Legends. Any certificates which evidence the shares of Restricted Stock shall bear the following legend (and such other restrictive legends as are required or deemed advisable under the provisions of any applicable law):

“THE SHARES OF COMMON STOCK EVIDENCED BY THIS CERTIFICATE ARE SUBJECT TO CERTAIN TRANSFER AND FORFEITURE RESTRICTIONS AS SET FORTH IN THAT CERTAIN RESTRICTED STOCK AWARD AGREEMENT BETWEEN THE COMPANY AND THE STOCKHOLDER, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF THE COMPANY. ANY ATTEMPTED TRANSFER OF SHARES OF COMMON STOCK EVIDENCED BY THIS CERTIFICATE IN VIOLATION OF SUCH AGREEMENT SHALL BE NULL AND VOID AND WITHOUT EFFECT.”

8. Continuance of Employment or Other Service. Nothing in this Agreement shall be deemed to create any obligation on the part of the Company or its affiliates to continue the employment or other service of Participant or interfere with the right of the Company or its affiliates to terminate the employment or service of Participant.

9. Provisions of the Plan. The provisions of the Plan, the terms of which are incorporated in this Agreement, shall govern if and to the extent that there are inconsistencies between those provisions and the provisions hereof. Participant acknowledges receipt of a copy of the Plan prior to the date of this Agreement.

10. Withholding.

(a) As a condition to the lifting or lapse of restrictions on this Award, or in connection with any other event that gives rise to a federal or other governmental tax withholding obligation on the part of the Company relating to this Award, (a) the Company may deduct or withhold (or cause to be deducted or withheld) from any payment or distribution to Participant, whether or not pursuant to the Plan, (ii) the Committee shall be entitled to require that Participant remit cash to the Company, or (iii) the Company may enter into any other suitable arrangements to withhold, in each case in an amount sufficient in the opinion of the Company to satisfy such withholding obligation.

(b) Unless the Company notifies you in writing before any Vesting Date, the number of Restricted Shares necessary to satisfy statutory withholding tax obligations on the Vesting Date will be released by you on the Vesting Date to an intermediary and sold in order to satisfy the withholding tax obligation. You will be responsible for standard, third-party administration processing fees in connection with such sale. In addition, you may be subject to and taxed in respect of short term capital gains or losses that reflect the difference in the withholding tax liability determined on the Vesting Date and the sales price actually achieved.

(c) This Award shall be subject to the provisions of Section 10(d) of the Plan.

11. Miscellaneous. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and their respective successors and permitted assigns. This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without regard to its principles of conflicts of law. This Agreement constitutes the entire agreement between the parties with respect to the subject matter hereof and, except as otherwise provided in the Plan, may not be modified other than by written instrument executed by the parties.

IN WITNESS WHEREOF, this Agreement has been executed as of the date first above written.

Exhibit A

FORM OF

STOCK POWER AND ASSIGNMENT

SEPARATE FROM CERTIFICATE

STOCK POWER AND ASSIGNMENT

SEPARATE FROM CERTIFICATE

FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers unto _____________________________________ _________________________, ________________ (            ) shares of Common Stock of Alexion Pharmaceuticals, Inc., a Delaware corporation, standing in the undersigned’s name on the books of said corporation represented by certificate number(s)             , and does hereby irrevocably constitute and appoint                              as attorney-in-fact, with full power of substitution, to transfer said stock on the books of said corporation.

This Stock Power and Assignment Separate from Certificate is being executed in conjunction with the terms of a Restricted Stock Award Agreement dated as of                  (the “Award Agreement”). The undersigned hereby acknowledges that the undersigned has received a copy of the Award Agreement and agrees to be bound by its terms.

INSTRUCTIONS: Please do not complete any blanks other than the “Signature” and “Printed Name” lines. Do not insert the Date on this assignment.