<?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>0001207793</rptOwnerCik>
            <rptOwnerName>BERGHEIM OLAV</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>
            <isOfficer>true</isOfficer>
            <officerTitle>CEO</officerTitle>
        </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>212053</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>212053</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Fjordinvest LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <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>22081</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>22081</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Micro NV LLC</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Pursuant to the business combination (the &quot;Business Combination&quot;) contemplated by the Business Combination Agreement, 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. Securities0 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 indirectly by the reporting person prior to the completion of the Business Combination.</footnote>
        <footnote id="F2">Shares held by Fjordinvest LLC. The reporting person is the President of Fjordinvest LLC and, as such, has voting and investment discretion over the shares held by Fjordinvest LLC.</footnote>
        <footnote id="F3">Shares held by Micro NV LLC. The reporting person is the President of Micro NV LLC and, as such, has voting and investment discretion over the shares held by Micro NV LLC.</footnote>
    </footnotes>

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