RESTRICTED STOCK UNIT AGREEMENT UNDER THE 2003 LONG-TERM INCENTIVE PLANAS AMENDED

Exhibit 10.A

RESTRICTED STOCK UNIT AGREEMENT UNDER THE

2003 LONG-TERM INCENTIVE PLAN AS AMENDED

THIS AGREEMENT is made as of the      day of                     , 20     by and between Sigma-Aldrich Corporation (“Company”) and                      (“Awardee”).

WHEREAS, the Board of Directors of the Company (“Board of Directors”) has adopted and the shareholders of the Company have approved the 2003 Long-Term Incentive Plan, as amended (“Plan”) pursuant to which Other Stock-Based Awards, including Awards pursuant to which common stock of the Company (“Common Stock”) may be acquired by employees of the Company and its subsidiaries in the future; and

WHEREAS, the Company desires to make a restricted stock unit award to the Awardee of                      (            ) restricted stock units under the terms hereinafter set forth:

NOW, THEREFORE, in consideration of the premises, and of the mutual agreements hereinafter set forth, it is covenanted and agreed as follows:

1. Award Subject to Plan. This award is made under, and is expressly subject to, all the terms and provisions of the Plan, a copy of which has been given to Awardee and which terms are incorporated herein by reference.

2. Terms of Award. Pursuant to action of the Compensation Committee of the Board of Directors, which action was made effective on                     , 20     (“Date of Award”), the Company awards to the Awardee                      (            ) restricted stock units (“Restricted Stock Units”), subject to the terms, conditions, and adjustments set forth in this Restricted Stock Unit Agreement (“Agreement”) and the Plan. Each Restricted Stock Unit represents the right to receive one share of the Common Stock of the Company (“Share”) to be issued and delivered at the end of the Vesting Period, subject to the risk of forfeiture described herein. The Restricted Stock Units are subject to forfeiture and cancellation without payment therefore for a period commencing on the Date of Award and ending on February 1, 2013 (“Vesting Period”), in the event the following occurs:

In the event either of the foregoing forfeiture triggers shall occur, the Restricted Stock Units shall not vest and shall become forfeited for no value and without any issuance of Shares. If neither of the above described forfeiture triggers occurs during the Vesting Period, the Restricted Stock Units shall become fully vested and the Shares underlying such Restricted Stock Units will be automatically issued and delivered on the last day of the Vesting Period, provided that the Awardee remains employed with the Company through such date.

3. Effect of Change of Control or Termination without Cause, Disability or Death. In the event of the Awardee’s termination of employment on account of an involuntary termination of employment by the Company without Cause, death, or Disability while employed with the Company during the Vesting Period, a pro rata portion of all of the Restricted Stock Units described in Section 2 above shall vest, and the Shares underlying such Restricted Stock Units will be automatically issued and delivered on the date of such termination of employment. Such prorated amount shall be based on the number of months in the Vesting Period during which the Awardee is employed with the Company, and the Awardee shall be deemed to be employed for an entire month if the Awardee is so involuntarily terminated, dies or suffers a Disability during such month while employed during the Vesting Period. Upon the occurrence of a Change in Control while the Awardee is employed with the Company during the Vesting Period, all of the Restricted Stock Units described in Section 2 above shall vest, and the Shares underlying such Restricted Stock Units will be automatically issued and delivered on the earlier of the Awardee’s termination of employment with the Company or the last day of the Vesting Period.

4. No Shareholder Rights. No rights of a shareholder shall exist with respect to the Restricted Stock Units as a result of the mere grant of the Restricted Stock Units. Such rights shall exist only after issuance of the Shares. Without limiting the foregoing, the Awardee shall not be entitled to receive, currently or on a deferred basis, any payments equivalent to cash, stock or other property paid by the Company as dividends on the Company’s common stock prior to the issuance of the Shares.

5. Withholding. The Awardee is responsible for any taxes required to be withheld under Federal, state, or local law in connection with the vesting of the Restricted Stock Units, the issuance and delivery of Shares to the Awardee, or any other event occurring pursuant to this Restricted Stock Unit Agreement or the Plan. The Company shall withhold from any payment hereunder an amount of Shares sufficient to cover any required withholding taxes due at the time such Shares are otherwise due to be issued and delivered hereunder to the extent required by minimum statutory withholding requirements.

6. Clawback. In the event the Board of Directors of the Company determines that the Awardee engaged in intentional conduct for the period commencing on February 1, 2013 and for two years thereafter ending January 31, 2015 and such conduct caused or substantially caused the Company to restate the Company’s financial statements as filed with the Securities and Exchange Commission, then the Awardee shall pay to the Company the amount equal to the difference of the value of the Shares as awarded on February 1, 2013 less any personal income taxes paid thereon.

7. Definitions; Copy of Plan. To the extent not specifically defined in this Agreement all capitalized terms used in this Agreement will have the same meanings ascribed to them in the Plan. By execution of this Agreement, the Awardee acknowledges receipt of a copy of the Plan.

8. Board Administration. This award has been made pursuant to a determination made by the Compensation Committee of the Board of Directors, and such Committee or any successor or substitute authorized in accordance with the Plan, and subject to the express terms of this Agreement, shall have plenary authority to interpret any provision of this Agreement and to make any determinations necessary or advisable for the administration of this Agreement and may waive or amend any provisions hereof in accordance with the Plan.

9. Amendment. This Agreement may be amended, in whole or in part, at any time by the Compensation Committee in accordance with the Plan.

10. Non-Transferability. This Restricted Stock Unit Award may not be assigned, transferred, or in any way encumbered except by will or the laws of descent and distribution.

11. Section 409A. It is intended that this Agreement shall be administered in a manner that will comply with or meet an exception from Section 409A of the Code, and this Agreement shall be administered and interpreted in accordance with such intent. The Committee may adopt rules deemed necessary or appropriate to qualify for an exception from or to comply with the requirements of Section 409A of the Code. Notwithstanding anything in this Section to the contrary, no amendment to or payment under this Agreement will be made unless permitted under Section 409A of the Code. If any amount shall be payable hereunder as a result of the Awardee’s “separation from service” at such time as the Awardee is a “specified employee” (as those terms are defined for purposes of Section 409A of the Code) and such amount is subject to the provisions of Section 409A of the Code, then no payment shall be made, except as permitted under Section 409A of the Code, prior to the first day of the seventh calendar month beginning after the Awardee’s separation from service, provided that, payment shall be made sooner upon the date of the Awardee’s earlier death following such separation from service.

IN WITNESS WHEREOF, the Company has caused this Agreement to be executed on its behalf, and the Awardee has signed this Agreement to evidence the Awardee’s acceptance of the terms hereof, all as of the date first above written.