<?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>0001722234</rptOwnerCik>
            <rptOwnerName>Agger Mette Kirstine</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>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Series C Preferred Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>776307</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The Series C Preferred Stock and the dividends that have accrued thereon to date are convertible on a 9.5-for-one basis into the number of shares of Common Stock shown in Column 3 without payment of further consideration at the holder's election or automatically upon the closing of the Issuer's initial public offering. The number of shares of Common Stock into which the Series C Preferred Stock and accrued dividends thereon are convertible will increase on a daily basis without payment of further consideration as additional dividends accrue. The shares have no expiration date.</footnote>
        <footnote id="F2">These shares are directly held by Lundbeckfond Invest A/S. The reporting person is the Managing Partner at Lundbeckfonden Ventures, which is the General Partner of Lundbeckfond Invest A/S. The reporting person disclaims beneficial ownership of such shares except to the extent of her pecuniary interest, if any, and this report shall not be deemed an admission that the reporting person is the beneficial owner of all of the reported shares for purposes of Section 16 or any other purpose.</footnote>
    </footnotes>

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

    <ownerSignature>
        <signatureName>/s/ Mette Kirstine Agger</signatureName>
        <signatureDate>2019-05-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
