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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2024-07-31</periodOfReport>

    <issuer>
        <issuerCik>0002006986</issuerCik>
        <issuerName>Adagio Medical Holdings, Inc.</issuerName>
        <issuerTradingSymbol>ADGM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001665442</rptOwnerCik>
            <rptOwnerName>Cox James L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O ADAGIO MEDICAL HOLDINGS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>26051 MERIT CIRCLE, SUITE 102</rptOwnerStreet2>
            <rptOwnerCity>LAGUNA HILLS</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92653</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>true</isDirector>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>false</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2024-07-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>36698</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>36698</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the business combination (the &quot;Business Combination&quot;) contemplated by the Business Combination Agreement (the &quot;BCA&quot;), dated February 13, 2024, as amended, by and among Adagio Medical Holdings, Inc. (formerly known as Aja Holdco Inc., &quot;New Adagio&quot; and following the completion of the Business Combination, the &quot;Issuer&quot;), ARYA Sciences Acquisition Corp IV, Adagio Medical, Inc. (&quot;Adagio&quot;) and certain other parties thereto, as described in the Registration Statement on Form S-4 (File No. 333-278811) filed with the U.S. Securities and Exchange Commission and declared effective on July 12, 2024, acquired by the reporting person in exchange for the shares of Adagio common stock held by the reporting person prior to the completion of the Business Combination.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ John Dahldorf, Attorney-in-Fact</signatureName>
        <signatureDate>2024-08-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
