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                                                                   EXHIBIT 3.1

                              AMENDED AND RESTATED

                          CERTIFICATE OF INCORPORATION

                                       OF

                      PRAECIS PHARMACEUTICALS INCORPORATED


            PRAECIS PHARMACEUTICALS INCORPORATED, a Delaware corporation (the
"Corporation"), does hereby certify that the Corporation was organized in the
State of Delaware on July 16, 1993 under the name Pharmaceutical Peptides, Inc.
and that this Amended and Restated Certificate of Incorporation hereby amends,
restates and integrates the provisions of the Amended and Restated Certificate
of Incorporation of the Corporation, as amended, as currently in effect (the
"Certificate of Incorporation"), and has been duly adopted in accordance with
the provisions of Sections 228, 242 and 245 of the General Corporation Law of
the State of Delaware by written consent of the holders of not less than a
majority of the outstanding stock of the Corporation entitled to vote thereon
and not less than a majority of each class of the outstanding stock of the
Corporation entitled to vote thereon. The text of the Certificate of
Incorporation is hereby amended and restated to read in its entirety as follows:

            FIRST: The name of the Corporation is PRAECIS PHARMACEUTICALS
INCORPORATED (hereinafter the "Corporation").

            SECOND: The address of the registered office of the Corporation in
the State of Delaware is 1209 Orange Street, in the City of Wilmington, County
of New Castle. The name of the Corporation's registered agent at that address is
The Corporation Trust Company.

            THIRD: The purpose of the Corporation is to engage in any lawful act
or activity for which a corporation may be organized under the General
Corporation Law of the State of Delaware as set forth in Title 8 of the Delaware
Code (the "DGCL").

            FOURTH: The total number of shares of stock which the Corporation
shall have authority to issue is (i) 200,000,000 shares of common stock, each
having a par value of one penny ($.01) ("Common Stock"), and (ii) 10,000,000
shares of preferred stock, each having a par value of one penny ($.01)
("Preferred Stock").
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A.    COMMON STOCK

            (1) Relative Rights of Preferred Stock and Common Stock. All
preferences, voting powers, relative, participating, optional or other special
rights and privileges and qualifications, limitations or restrictions of the
Common Stock are expressly made subject to those that may be fixed with respect
to any shares of Preferred Stock.

            (2) Voting Rights. Except as otherwise required by law or this
Amended and Restated Certificate of Incorporation, each holder of shares of
Common Stock shall be entitled to one vote for each share of Common Stock
standing in his name on the books of the Corporation on the record date for the
determination of stockholders entitled to notice of, or to vote at, any meeting
of stockholders of the Corporation. There shall be no cumulative voting.

            (3) Dividends. Subject to the preferential rights of holders of
Preferred Stock, if any, the holders of shares of Common Stock shall be entitled
to receive, when and if declared by the Board of Directors of the Corporation
(the "Board of Directors"), out of the assets of the Corporation which are by
law available therefor, dividends payable either in cash, or in property or
shares of capital stock, notes or other evidence of indebtedness, of the
Corporation or any other person or entity.

            (4) Dissolution, Liquidation or Winding Up. In the event of any
voluntary or involuntary liquidation, dissolution or winding up of the
Corporation, after distribution in full of the preferential amounts, if any, to
be distributed to the holders of shares of Preferred Stock, unless otherwise
required by law, holders of shares of Common Stock shall be entitled to receive
all the remaining assets of the Corporation of whatever kind available for
distribution to stockholders ratably in proportion to the number of shares of
Common Stock held by them respectively.

B.    PREFERRED STOCK

            (1) General. The Board of Directors is expressly authorized to
provide for the issuance of all or any shares of the Preferred Stock in one or
more classes or series, and to fix for each such class or series such voting
powers, full or limited, or no voting powers, and such distinctive designations,
preferences and relative, participating, optional or other special rights and
such qualifications, limitations or restrictions thereof, as shall be stated and
expressed in the resolution or resolutions adopted by the Board of Directors
providing for the issuance of such class or series and as may be permitted by
the DGCL, including, without limitation, the authority to provide that any such
class or series may be (a) subject to redemption at such time or times and at
such price or prices; (b) entitled to receive dividends (which may be cumulative
or non-cumulative) at such rates, on such conditions, and at such times,


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and payable in preference to, or in such relation to, the dividends payable on
any other class or classes or any other series; (c) entitled to such rights upon
the dissolution, liquidation or winding-up of, or upon any distribution of the
assets of, the Corporation; or (d) convertible into, or exchangeable for, shares
of any other class or classes of stock, or of any other series of the same or
any other class or classes of stock, at such price or prices or at such rates of
exchange and with such adjustments; all as may be stated in such resolution or
resolutions.

            FIFTH: The following provisions are inserted for the management of
the business and the conduct of the affairs of the Corporation, and for further
definition, limitation and regulation of the powers of the Corporation and of
its directors and stockholders:

            (1) The business and affairs of the Corporation shall be managed by
or under the direction of the Board of Directors.

            (2) The number of directors that shall constitute the whole Board of
Directors shall from time to time be fixed exclusively by the Board of Directors
by a resolution adopted by a majority of the whole Board of Directors serving at
the time of adoption of such resolution. In no event shall the number of
directors that constitute the whole Board of Directors be less than three. No
decrease in the number of directors shall have the effect of shortening the term
of any incumbent director. Election of directors need not be by written ballot
unless the By-Laws so provide.

            (3) In addition to the powers and authority hereinbefore or by
statute expressly conferred upon them, the directors are hereby empowered to
exercise all such powers and do all such acts and things as may be exercised or
done by the Corporation, subject, nevertheless, to the provisions of the DGCL,
this Amended and Restated Certificate of Incorporation and the By-Laws.

            (4) Any vacancy on the Board of Directors that results from an
increase in the number of directors may be filled only by a majority of the
directors then in office, provided that a quorum is present, and any other
vacancy occurring in the Board of Directors may be filled only by a majority of
the directors then in office, even if less than a quorum, or by a sole remaining
director. Any director elected to fill a vacancy not resulting from an increase
in the number of directors shall have the same remaining term as that of his
predecessor and shall hold office until his successor shall be duly elected and
shall duly qualify, subject, however, to prior death, resignation, retirement,
disqualification or removal from office.

            (5) Notwithstanding the foregoing, whenever the holders of any one
or more classes or series of Preferred Stock issued by the Corporation shall
have the right, voting separately by class or series, to elect directors at an
annual or special


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meeting of stockholders, the election, term of office, filling of vacancies,
removal and other features of such directorships shall be governed by the terms
of the instrument creating such class or series of Preferred Stock.

            (6) The presence of a majority of the total number of directors
shall constitute a quorum for the transaction of business and, except as
otherwise provided herein, the vote of a majority of such quorum shall be
required in order for the Board of Directors to act.

            SIXTH: Any action required or permitted to be taken by the
stockholders of the Corporation must be effected at a duly called annual or
special meeting of stockholders of the Corporation, and the ability of the
stockholders to consent in writing to the taking of any action is hereby
specifically denied.

            SEVENTH: Unless otherwise required by law, special meetings of
stockholders, for any purpose or purposes, may be called only by (i) the
Chairman of the Board of Directors, if there be one, (ii) the President, (iii)
any Vice President, if there be one, (iv) the Secretary or (v) any Assistant
Secretary, if there be one, and shall be called by any such officer pursuant to
a resolution adopted by a majority of the Board of Directors. Stockholders shall
not be entitled to call a special meeting of stockholders, nor to require the
Board of Directors to call such a special meeting.

            EIGHTH: In furtherance and not in limitation of the powers conferred
by the laws of the State of Delaware, the Board of Directors is expressly
authorized and empowered to adopt, amend or repeal any provision of the By-Laws
of the Corporation. The By-Laws of the Corporation may be adopted, amended or
repealed by the stockholders by the affirmative vote of holders of shares
representing at least two-thirds (66 2/3%) of the voting power of all shares
entitled to vote at an election of directors.

            NINTH: The Corporation shall indemnify its directors and officers to
the fullest extent authorized or permitted by law, as now or hereafter in
effect, and such right to indemnification shall continue as to a person who has
ceased to be a director or officer of the Corporation and shall inure to the
benefit of his or her heirs, executors and personal and legal representatives;
provided however, that, except for proceedings to enforce rights to
indemnification, the Corporation shall not be obligated to indemnify or to
advance expenses to any director or officer (or his or her heirs, executors or
personal or legal representatives) in connection with a proceeding (or part
thereof) initiated by such person unless such proceeding (or part thereof) was
authorized or consented to by the Board of Directors. The right to
indemnification conferred by this Article NINTH shall include the right to be
paid by the Corporation the expenses incurred in defending or otherwise
participating in any proceeding in advance of its final disposition.


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            The Corporation may, to the extent authorized from time to time by
the Board of Directors, provide rights to indemnification and to the advancement
of expenses to employees and agents of the Corporation similar to those
conferred in this Article NINTH to directors and officers of the Corporation.

            The rights to indemnification and to the advancement of expenses
conferred in this Article NINTH shall not be exclusive of any other right which
any person may have or hereafter acquire under this Amended and Restated
Certificate of Incorporation, the By-Laws of the Corporation, any statute,
agreement, vote of stockholders or disinterested directors or otherwise.

            Any repeal or modification of this Article NINTH or Article VIII of
the By-Laws of the Corporation shall not adversely affect any rights to
indemnification and the advancement of expenses of a director or officer of the
Corporation existing at the time of such repeal or modification with respect to
any acts or omissions occurring prior to such repeal or modification.

            TENTH: No director shall be personally liable to the Corporation or
any of its stockholders for monetary damages for breach of fiduciary duty as a
director, except to the extent such exemption from liability or limitation
thereto is not permitted under the DGCL as the same exists or may hereafter be
amended. If the DGCL is amended hereafter to authorize the further elimination
or limitation of the liability of directors, then the liability of a director of
the Corporation shall automatically, without any required action by the
Corporation or any other person, be eliminated or limited to the fullest extent
authorized by the DGCL, as so amended. Any repeal or modification of this
Article TENTH shall not adversely affect any right or protection of a director
of the Corporation existing at the time of such repeal or modification with
respect to acts or omissions occurring prior to such repeal or modification.

            ELEVENTH: Meetings of stockholders may be held within or without the
State of Delaware, as the By-Laws may provide. The books of the Corporation may
be kept (subject to any provision contained in the DGCL) outside the State of
Delaware at such place or places as may be designated from time to time by the
Board of Directors or in the By-Laws of the Corporation.

            TWELFTH: The Corporation reserves the right to amend, alter, change
or repeal any provision contained in this Amended and Restated Certificate of
Incorporation, in the manner now or hereafter prescribed by statute, and all
rights conferred upon stockholders herein are granted subject to this
reservation; provided, however, that, notwithstanding any other provision of
this Amended and Restated Certificate of Incorporation (and in addition to any
other vote that may be the DGCL), the affirmative vote of holders of at least
eighty-five percent (85%) of the voting power of the shares entitled to vote for
the election of directors, shall be re-


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quired to amend, alter, change or repeal any provision of, or to adopt any
provision as part of this Amended and Restated Certificate of Incorporation
inconsistent with the purpose and intent of, Articles SIXTH, SEVENTH, EIGHTH,
NINTH or TENTH of this Amended and Restated Certificate of Incorporation or this
Article TWELFTH.


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            IN WITNESS WHEREOF, PRAECIS PHARMACEUTICALS INCORPORATED has caused
this Amended and Restated Certificate of Incorporation to be executed in its
corporate name this 2nd day of May, 2000.

                              PRAECIS PHARMACEUTICALS
                                    INCORPORATED


                              By: /s/ Malcolm L. Gefter
                                  --------------------------------------
                                 Malcolm L. Gefter
                                 Chairman of the Board, Chief Executive
                                   Officer and President


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