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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-07-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000896159</issuerCik>
        <issuerName>Chubb Ltd</issuerName>
        <issuerTradingSymbol>CB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001866747</rptOwnerCik>
            <rptOwnerName>Enns Peter C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>THE CHUBB BUILDING</rptOwnerStreet1>
            <rptOwnerStreet2>17 WOODBOURNE AVENUE</rptOwnerStreet2>
            <rptOwnerCity>HAMILTON</rptOwnerCity>
            <rptOwnerState>D0</rptOwnerState>
            <rptOwnerZipCode>HM 08</rptOwnerZipCode>
            <rptOwnerStateDescription>BERMUDA</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Executive Vice President and*</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26136</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Options to Acquire</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>158.99</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-04-01</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15095</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Included in the total are 13,587 shares of restricted stock granted pursuant to the Chubb Limited 2016 Long-Term Incentive Plan (the &quot;Plan&quot;).  These shares vests in equal installments on April 1, 2022, April 1, 2023, April 1, 2024 and April 1, 2025.</footnote>
        <footnote id="F2">Included in the total are 5,787 shares of restricted stock granted pursuant to the Plan.  These shares vests on April 1, 2024 subject to the satisfaction of certain service and performance based criteria.</footnote>
        <footnote id="F3">Included in the total are 3,762 shares of restricted stock granted pursuant to the Plan, representing a premium performance award with respect to the performance restricted stock awards. These shares vest on April 1, 2024 subject to the satisfaction of certain service and performance based criteria.  These shares will not be entitled to vote until vested. Dividends on these shares shall be accumulated and distributed only when, and to the extent, that the shares have vested.</footnote>
        <footnote id="F4">Options awarded pursuant to the plan.  Options vest in equal installments on April 1, 2022, April 1, 2023 and April 1, 2024.</footnote>
    </footnotes>

    <remarks>*Chief Financial Officer</remarks>

    <ownerSignature>
        <signatureName>/s/ Samantha Froud, Attorney-in-fact</signatureName>
        <signatureDate>2021-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
