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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

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

    <noSecuritiesOwned>0</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001224962</rptOwnerCik>
            <rptOwnerName>PERCEPTIVE ADVISORS LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>51 ASTOR PLACE, 10TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>true</isDirector>
            <isTenPercentOwner>true</isTenPercentOwner>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001249675</rptOwnerCik>
            <rptOwnerName>PERCEPTIVE LIFE SCIENCES MASTER FUND LTD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>51 ASTOR PLACE, 10TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isTenPercentOwner>true</isTenPercentOwner>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001164426</rptOwnerCik>
            <rptOwnerName>EDELMAN JOSEPH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PERCEPTIVE CAPITAL SOLUTIONS CORP</rptOwnerStreet1>
            <rptOwnerStreet2>51 ASTOR PLACE, 10TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isTenPercentOwner>true</isTenPercentOwner>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7160397</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>PIPE Warrants</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>10</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2024-07-31</value>
            </exerciseDate>
            <expirationDate>
                <value>2029-07-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5445069</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Convert Warrants</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>24</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2024-07-31</value>
            </exerciseDate>
            <expirationDate>
                <value>2031-07-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>525000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Convertible Notes</value>
                <footnoteId id="F3"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2024-07-31</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-04-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>700000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The securities are directly held by Perceptive Life Sciences Master Fund, Ltd. (the &quot;Master Fund&quot;). Perceptive Advisors LLC (the &quot;Advisor&quot;) serves as the investment manager of the Master Fund. Joseph Edelman (&quot;Mr. Edelman&quot;) serves as the managing member of the Advisor. Each of Mr. Edelman and the Advisor disclaim, for purposes of Section 16 of the Securities Exchange Act of 1934, beneficial ownership of such securities, except to the extent of their indirect pecuniary interest therein, and this report shall not be deemed an admission that the Advisor or Mr. Edelman are beneficial owner of such securities for purposes of Section 16 or for any other purposes.</footnote>
        <footnote id="F2">The Master Fund was issued 5,445,069 warrants (the &quot;PIPE Warrants&quot;) on July 29, 2024 pursuant to an Amended and Restated Subscription Agreement, dated July 29, 2024. Subject to adjustment, as provided in the Convert Warrants, each PIPE Warrant is exercisable for one share of common stock, par value $0.0001 per share (the &quot;Common Stock&quot;), of Adagio Medical Holdings, Inc. (f/k/a Aja HoldCo, Inc.) (the &quot;Issuer&quot;), at an exercise price of $10.00.</footnote>
        <footnote id="F3">The Master Fund was issued $7,000,000 in principal amount of convertible notes (&quot;Convertible Notes&quot;) and 525,000 warrants (&quot;Convert Warrants&quot;) of the Issuer on July 29, 2024. The Convertible Notes and any interest that compounds on the principal amount outstanding under the Convertible Notes are convertible into shares of Common Stock at the Master Fund's option at an initial conversion price of $10.00 per share. Subject to adjustment, as provided in the Convert Warrants, each Convert Warrant is exercisable for one share of Common Stock at an exercise price of $24.00.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Joseph Edelman - for Perceptive Advisors LLC,
By: Joseph Edelman, its managing member</signatureName>
        <signatureDate>2024-08-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Joseph Edelman - for Perceptive Life Sciences
Master Fund, Ltd., By: Perceptive Advisors LLC,
its investment manager, By: Joseph Edelman,
its managing member</signatureName>
        <signatureDate>2024-08-01</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Joseph Edelman</signatureName>
        <signatureDate>2024-08-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
