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

    <schemaVersion>X0607</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2026-08-19</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001837607</issuerCik>
        <issuerName>AEON Biopharma, Inc.</issuerName>
        <issuerTradingSymbol>AEON</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001270925</rptOwnerCik>
            <rptOwnerName>LYNCH TIMOTHY P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>70 SW CENTURY DR.</rptOwnerStreet1>
            <rptOwnerStreet2>STE. 100</rptOwnerStreet2>
            <rptOwnerCity>BEND</rptOwnerCity>
            <rptOwnerState>OR</rptOwnerState>
            <rptOwnerZipCode>97702</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>false</isDirector>
            <isOfficer>false</isOfficer>
            <isTenPercentOwner>true</isTenPercentOwner>
            <isOther>false</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5350000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Pre-Funded Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.0001</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1000000</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.3221</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2026-07-15</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                    <footnoteId id="F4"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000000</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Warrants</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.3704</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <value>2026-07-15</value>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                    <footnoteId id="F6"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000000</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The pre-funded warrants are exercisable at any time and have no expiration date.</footnote>
        <footnote id="F2">The reporting person (together with his affiliates) may not exercise any portion of these warrant to the extent that, after giving effect to such exercise, the reporting person would beneficially own more than 4.99% of the outstanding shares of Class A Common Stock immediately after exercise. The beneficial ownership limitation may be increased or decreased at the reporting person's election to a percentage not in excess of 19.99%, upon at least 61 days' prior written notice to us, subject to the terms of the warrants.</footnote>
        <footnote id="F3">These warrants will expire on the earlier of (i) the second anniversary of the date of issuance and (ii) the 45th day following the Issuer's public announcement that it has received Type 2B meeting minutes from the FDA regarding certain matters.</footnote>
        <footnote id="F4">At the option of the reporting person, each of these warrants may be exercised for either one share of Class A Common Stock or one pre-funded warrant to acquire Class A Common Stock.</footnote>
        <footnote id="F5">These warrants will expire on the earlier of (i) the fifth anniversary of the date of issuance and (ii) 45 days following the Issuer's public announcement that the Issuer has initiated a Phase 3 clinical equivalence trial of ABP-450 as a biosimilar to BOTOX.</footnote>
        <footnote id="F6">At the option of the reporting person, each of these warrants may be exercised for either one share of Class A Common Stock or one pre-funded warrant to acquire Class A Common Stock.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Timothy P. Lynch</signatureName>
        <signatureDate>2026-08-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
