<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2019-05-07</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001563880</issuerCik>
        <issuerName>Trevi Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>TRVI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001587852</rptOwnerCik>
            <rptOwnerName>Nadav Eran</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O TREVI THERAPEUTICS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>195 CHURCH STREET, 14TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW HAVEN</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06510</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>No securities beneficially owned</value>
                <footnoteId id="F1"/>
                <footnoteId id="F2"/>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Eran Nadav is a TPG Senior Advisor.  TPG is affiliated with TPG Biotechnology Partners III, L.P., which directly holds shares of the Issuer's preferred stock.</footnote>
        <footnote id="F2">Mr. Nadav disclaims beneficial ownership of all of the securities that are or may be beneficially owned by TPG Biotechnology Partners III, L.P. or any of its affiliates.  Pursuant to Rule 16a-1(a)(4) under the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;), this filing shall not be deemed an admission that Mr. Nadav is, for purposes of Section 16 of the Exchange Act or otherwise, the beneficial owner of any equity securities of the Issuer for purposes of Section 16 of the Exchange Act or otherwise.</footnote>
    </footnotes>

    <remarks>Exhibit Index: 24.1 Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/  Eran Nadav</signatureName>
        <signatureDate>2019-05-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
