Exhibit 3.1

CERTIFICATE OF AMENDMENT

TO THE

restated CERTIFICATE OF INCORPORATION

OF

TREVI THERAPEUTICS, INC.

(Pursuant to Section 242 of the
General Corporation Law of the State of Delaware)

Trevi Therapeutics, Inc. (the “Corporation”), a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (the “General Corporation Law”), does hereby certify as follows:

A resolution was duly adopted by the Board of Directors of the Corporation pursuant to Section 242 of the General Corporation Law setting forth a proposed amendment to the Corporation’s Restated Certificate of Incorporation (the “Certificate of Incorporation”), and declaring said amendment to be advisable. The stockholders of the Corporation duly approved said proposed amendment in accordance with Section 242 of the General Corporation Law. Accordingly, to effect such proposed amendment, it is

RESOLVED: That Article SEVENTH of the Certificate of Incorporation be and hereby is deleted in its entirety and the following is inserted in lieu thereof:

“SEVENTH: To the fullest extent permitted by the General Corporation Law of the State of Delaware, no director or officer of the Corporation shall be personally liable to the Corporation (in the case of directors) or its stockholders (in the case of directors and officers) for monetary damages for any breach of fiduciary duty as a director or officer. No amendment, repeal or elimination of this provision shall apply to or have any effect on its application with respect to any act or omission of a director or officer occurring before such amendment, repeal or elimination. If the General Corporation Law of the State of Delaware is amended to permit further elimination or limitation of the personal liability of directors or officers, then the liability of a director or officer of the Corporation shall be eliminated or limited to the fullest extent permitted by the General Corporation Law of the State of Delaware as so amended.”

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IN WITNESS WHEREOF, this Certificate of Amendment has been executed by a duly authorized officer of the Corporation on this 28th day of June, 2023.

TREVI THERAPEUTICS, INC.

By: /s/ Jennifer Good

Name: Jennifer Good

Title: Chief Executive Officer

[Signature Page to Certificate of Amendment]