Exhibit 4.1

FIRST AMENDMENT TO

RIGHTS AGREEMENT

This First Amendment to Rights Agreement, effective as of February 27, 2014 (the “Amendment”), amends the Rights Agreement, dated as of July 13, 2005 (the “Rights Agreement”), between Alnylam Pharmaceuticals, Inc., a Delaware corporation (the “Company”), and Computershare Trust Company, N.A., f/k/a Equiserve Trust Company, N.A., a national banking association (the “Rights Agent”). Capitalized terms used herein but not defined herein shall have their defined meanings set forth in the Rights Agreement.

WHEREAS, pursuant to the Stock Purchase Agreement between the Company and Genzyme Corporation, a Massachusetts corporation (the “Investor”), dated as of January 11, 2014, the Investor is acquiring 8,766,338 shares (the “Initial Shares”), or approximately 12%, of the outstanding common stock, par value $.01 per share (the “Common Stock”), of the Company as of the date thereof and after giving effect to such stock issuance;

WHEREAS, pursuant to the Investor Agreement by and between the Company and the Investor, dated as of February 27, 2014 (the “Investor Agreement”), the Company desires to amend the Rights Agreement to provide that the Investor and its Affiliates and Associates may acquire and beneficially own additional shares of Common Stock (together with the Initial Shares, the “Shares”) without becoming Acquiring Persons (as defined in the Rights Agreement), consistent with the terms of the Investor Agreement (the “Exemption”);

WHEREAS, as a condition to the willingness of the Company to agree to provide the Exemption to the Investor, the Investor has agreed to take certain actions and forebear from taking certain other actions, as set forth in the Investor Agreement;

WHEREAS, pursuant to Section 27 of the Rights Agreement and under the circumstances specified therein, the Company and the Rights Agent shall, if the Company so directs, supplement or amend any provision of the Rights Agreement in any respect without the approval of any holders of the Rights;

WHEREAS, the Company now desires to amend the Rights Agreement as set forth in this Amendment, and pursuant to Section 27 of the Rights Agreement, the Company hereby directs that the Rights Agreement should be amended as set forth in this Amendment; and

WHEREAS, the Board has determined that this Amendment and the transactions contemplated hereby are advisable and in the best interests of the Company and the holders of Common Stock.

NOW, THEREFORE, the parties hereby agree as follows:

1. Section 1 of the Rights Agreement is hereby amended by adding the following definitions:

(nn) “Genzyme Entities” shall mean Genzyme Corporation and its Affiliates and Associates.

(oo) “Investor Agreement” shall mean the Investor Agreement, dated February 27, 2014, by and between Genzyme Corporation and the Company.

(pp) “Standstill Limit” shall have the meaning set forth in the Investor Agreement.

(qq) “Standstill Term” shall have the meaning set forth in the Investor Agreement.

2. The definition of “Acquiring Person” in Section 1(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“Acquiring Person” shall mean any Person who or which, together with all Affiliates and Associates of such Person, shall be the Beneficial Owner of 20% or more of the shares of Common Stock then outstanding, but shall not include (i) the Company, (ii) any Subsidiary of the Company, (iii) any employee benefit plan of the Company or of any Subsidiary of the Company or (iv) any Person organized, appointed or established by the Company for or pursuant to the terms of any such plan. Notwithstanding the foregoing, (x) no Person shall become an “Acquiring Person” as the result of an acquisition of Common Stock by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares Beneficially Owned by such Person to 20% or more of the shares of Common Stock of the Company then outstanding; provided, however that if a Person shall become the Beneficial Owner of 20% or more of the shares of Common Stock of the Company then outstanding as the result of an acquisition of Common Stock by the Company and shall, following written notice from, or public disclosure by the Company of such share purchases by the Company become the Beneficial Owner of any additional Common Stock of the Company and shall then Beneficially Own 20% or more of the shares of Common Stock then outstanding, then such Person shall be deemed to be an “Acquiring Person”, (y) if the Board determines in good faith that a Person who would otherwise be an “Acquiring Person,” as defined pursuant to the foregoing provisions of this paragraph (a), has become such inadvertently, and such Person divests as promptly as practicable (as determined in good faith by the Board of Directors) following receipt of written notice from the Company of such event, of Beneficial Ownership of a sufficient number of shares of Common Stock so that such Person would no longer be an “Acquiring Person,” as defined pursuant to the foregoing provisions of this paragraph (a), then such Person shall not be deemed to be an “Acquiring Person” for any purposes of this Agreement unless and until such Person shall again become an “Acquiring Person” and (z) the term “Acquiring Person” shall not include (i) during the Standstill Term (as it may be reinstated pursuant to the proviso in Section 1(ppp) of the Investor Agreement or extended pursuant to Section 3.2(c) of the Investor Agreement), the Genzyme Entities provided and only for so long as the Genzyme Entities do not collectively Beneficially Own shares of Common Stock of the Company in excess of the Standstill Limit (as

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adjusted pursuant to Section 3.2(c) of the Investor Agreement and except as otherwise permitted by the proviso in Section 3.1(a) of the Investor Agreement) and (ii) after the Standstill Term, in the event that the Genzyme Entities collectively Beneficially Own 20% or more of the then outstanding shares of Common Stock of the Company as of the expiration or termination of the Standstill Term (including any reinstated Standstill Term pursuant to the proviso in Section 1(ppp) of the Investor Agreement), the Genzyme Entities but only so long as they collectively Beneficially Own a number of shares of Common Stock of the Company equal to the number of shares of Common Stock of the Company collectively Beneficially Owned by the Genzyme Entities as of the expiration or termination of the Standstill Term minus any shares of Common Stock of the Company thereafter sold, transferred or otherwise disposed of by a Genzyme Entity plus any additional shares of Common Stock of the Company acquired by a Genzyme Entity solely as provided by Section 6 of the Investor Agreement until such right shall have terminated in accordance with the terms of the Investor Agreement. For the avoidance of doubt, if after expiration or termination of the Standstill Term the Genzyme Entities shall collectively Beneficially Own less than 20% of the shares of Common Stock of the Company then outstanding and no longer have the right pursuant to Section 6 of the Investor Agreement to acquire additional shares of Common Stock of the Company that would permit the Genzyme Entities to maintain Beneficial Ownership of Common Stock of the Company equal to 20% or more of the shares then outstanding, then the exclusion of the Genzyme Entities from the definition of “Acquiring Person” provided in the foregoing clause (z)(ii) shall terminate.

3. Section 3(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

Until the earlier of (i) the close of business on the tenth Business Day (or such later date as may be determined by the Board) after the Stock Acquisition Date (or, if the tenth Business Day after the Stock Acquisition Date occurs before the Record Date, the close of business on the Record Date), or (ii) the close of business on the tenth Business Day (or such later date as may be determined by action of the Board) after the date that a tender or exchange offer (other than a Permitted Offer) is first published or sent or given within the meaning of Rule 14d-2 of the General Rules and Regulations under the Exchange Act, by (A) any Person (other than the Company, any Subsidiary of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company, any Person organized, appointed or established by the Company for or pursuant to the terms of any such plan, or, during the Standstill Term (as it may be reinstated pursuant to the proviso in Section 1(ppp) of the Investor Agreement or extended pursuant to Section 3.2(c) of the Investor Agreement), the Genzyme Entities) if upon consummation thereof, such Person would be the Beneficial Owner of 20% or more of the shares of Common Stock then outstanding, or (B) the Genzyme Entities, during the Standstill Term (as it may be reinstated pursuant to the proviso in Section 1(ppp) of the Investor Agreement or extended pursuant to Section 3.2(c) of the Investor Agreement), if upon consummation thereof the Genzyme Entities would collectively Beneficially Own shares of Common Stock of the Company in excess of the Standstill Limit (as adjusted pursuant to Section 3.2(c)

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of the Investor Agreement) (the earlier of (i) and (ii) being herein referred to as the “Distribution Date”), (x) the Rights will be evidenced by the certificates for the Common Stock registered in the names of the holders of the Common Stock (which certificates for Common Stock shall be deemed also to be certificates for Rights) and not by separate certificates, and (y) the Rights will be transferable only in connection with the transfer of the underlying shares of Common Stock (including a transfer to the Company). As soon as practicable after the Distribution Date, the Rights Agent will send by first-class, insured, postage prepaid mail, to each record holder of the Common Stock as of the close of business on the Distribution Date, at the address of such holder shown on the records of the Company, one or more rights certificates, in substantially the form of Exhibit B hereto (the “Rights Certificates”), evidencing one Right for each share of Common Stock so held, subject to adjustment as provided herein. With respect to certificates for the Common Stock outstanding as of the close of business on the Record Date, until the Distribution Date, the Rights will be evidenced by such certificates for the Common Stock and the registered holders of the Common Stock shall also be the registered holders of the associated Rights. In addition, in connection with the issuance or sale of shares of Common Stock following the Distribution Date and prior to the redemption or expiration of the Rights, the Company (i) shall, with respect to shares of Common Stock so issued or sold pursuant to the exercise of stock options or under any employee benefit plan or arrangement, or upon the exercise, conversion or exchange of securities granted or issued by the Company prior to the Distribution Date, and (ii) may, in any other case, if deemed necessary or appropriate by the Board, issue Rights Certificates representing the appropriate number of Rights in connection with such issuance or sale; provided, however, that (x) no such Rights Certificate shall be issued if, and to the extent that, the Company shall be advised by counsel that such issuance would create a significant risk of material adverse tax consequences to the Company or the Person to whom such Rights Certificate would be issued, and (y) no such Rights Certificate shall be issued if, and to the extent that, appropriate adjustment shall otherwise have been made in lieu of the issuance thereof. In the event that an adjustment in the number of Rights per share of Common Stock has been made pursuant to Sections 11(i) or 11(p) hereof, at the time of distribution of the Rights Certificates, the Company shall make the necessary and appropriate rounding adjustments (in accordance with Section 14(a) hereof) so that Rights Certificates representing only whole numbers of Rights are distributed and cash is paid in lieu of any fractional Rights. As of and after the Distribution Date, the Rights will be evidenced solely by such Rights Certificates.

4. Except as expressly set forth herein, this Amendment shall not by implication or otherwise alter, modify, amend or in any way affect any of the terms, conditions, obligations, covenants or agreements contained in the Rights Agreement, all of which are ratified and affirmed in all respects and shall continue in full force and effect and shall be otherwise unaffected.

5. This Amendment shall be governed by and construed in accordance with the laws of the State of Delaware, United States of America, applicable to contracts made and to be performed entirely within such State, without regard to conflict-of-law principles.

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6. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Amendment transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

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IN WITNESS WHEREOF, the parties have caused this Amendment to be duly executed as of the day and year first above written.

[Signature Page to First Amendment to Rights Agreement]