THIRD AMENDMENT AND WAIVER (A$ Credit Agreement)

Exhibit 10.3

EXECUTION COPY

THIRD AMENDMENT AND WAIVER

(A$ Credit Agreement)

THIRD AMENDMENT AND WAIVER dated as of 10 July 2008 (this “Amendment”) amends the Credit Agreement dated as of 13 December 2005, as amended on 22 June 2007 and as amended and restated on 19 December 2007 pursuant to an Amendment and Restatement Agreement dated as of 14 December 2007 (as so amended and restated, the “Credit Agreement”) among ACE Australia Holdings Pty Limited (the “Borrower”), ACE Limited (the “Guarantor”), various financial institutions and The Royal Bank of Scotland plc, as Agent. Capitalized terms used but not defined herein have the respective meanings set forth in the Credit Agreement.

WHEREAS, the Guarantor has informed the Agent that the Guarantor expects to re-domesticate to move its place of incorporation from the Cayman Islands to Switzerland; and

WHEREAS, the Guarantor has requested and the parties have agreed to amend the Credit Agreement in certain respects as more fully set forth below.

NOW, THEREFORE, the parties hereto agree as follows:

SECTION 1. Amendments to Credit Agreement. Subject to the conditions set forth in Section 4, the Credit Agreement is amended as set forth in this Section 1.

1.1 Clause 2.2 is amended by adding the following immediately before the period at the end thereof: “, provided that no amount borrowed under this Facility may be used directly or indirectly in Switzerland”.

1.2 Clause 15.5 is amended by adding the following phrase immediately before the period at the end thereof “or if such disclosure would violate any applicable law”.

1.3 Clause 29.3.1 is amended by (a) deleting the phrase “to a Subsidiary of the Guarantor” that begins in the eighth to last line thereof and substituting the phrase “to a Wholly-Owned Consolidated Subsidiary of the Guarantor that is not organized under the laws of Switzerland” therefor; (b) deleting the phrase “that Subsidiary” that begins in the third to last line thereof and substituting the phrase “that Wholly-Owned Consolidated Subsidiary”; and (c) adding the following immediately before the period at the end thereof: “; provided that (notwithstanding any other provision of this Agreement to the contrary) so long as the Guarantor is incorporated under the laws of Switzerland, the Guarantor may not be the Borrower Transferee without the prior written consent of all Finance Parties”.

1.4 Clause 29.3.2(b) is amended by deleting the phrase “Subsidiary of the Guarantor” each time it appears therein and substituting the phrase “Wholly-Owned Consolidated Subsidiary of the Guarantor” therefor.

SECTION 2. Waiver. The Majority Banks waive any Default that may arise under Clause 15.4 (Preservation of Corporate Existence) of the Credit Agreement upon the re-domestication of the Guarantor to move its place of incorporation from the Cayman Islands to Switzerland in the third or fourth quarter of 2008 (the “Re-domestication”).

SECTION 3. Representations and Warranties. Each Obligor represents and warrants as follows:

3.1 Authorization. The execution, delivery and performance by such Obligor of this Amendment are within its corporate powers, have been duly authorised by all necessary corporate action, require no action by or in respect of, or filing with, any governmental body, agency or official and do not contravene, or constitute a default under, any provision of applicable law or regulation or of the memorandum of association, articles of association or by-laws (or any comparable document) of such Obligor or of any material agreement, judgment, injunction, order, decree or other instrument binding upon such Obligor or any of its Subsidiaries or result in the creation or imposition of any Lien on any asset of such Obligor or any of its Subsidiaries.

3.2 Enforceability. This Amendment constitutes a legal, valid and binding obligation of such Obligor enforceable against such Obligor in accordance with its terms, subject to bankruptcy, insolvency or other laws of general application affecting the enforcement of creditors’ rights, the application of equitable principles, the non-availability of the equitable remedies of specific performance or injunctive relief and, with respect to matters of Swiss law, the limitations and qualifications set forth in the opinion letter referred to in Section 5 below.

3.3 Representations and Warranties; No Default. After giving effect to this Amendment: (a) each representation and warranty of such Obligor contained in Clauses 13 and 14, as applicable, of the Credit Agreement is true and correct on and as of the date hereof with the same effect as if made on and as of the date hereof (except to the extent any such representation or warranty is expressly stated to have been made as of a specific date, in which case such representation or warranty was true and correct as of such date) and (b) no Default has occurred and is continuing.

SECTION 4. Effectiveness of Amendment. This Amendment (including the waiver set forth in Section 2) shall become effective as of the date set forth above when the Agent has (a) received the consent of the Majority Banks to the amendment and waiver contemplated herein, (b) signed a counterpart hereof and (c) received counterparts hereof signed by the Obligors; provided that the amendments set forth in Section 1 shall not become effective until the occurrence of the Re-domestication.

SECTION 5. Post-Closing Requirements. The Guarantor agrees that it will, within three Business Days after the effectiveness of the Re-domestication, deliver to the Agent (a) copies of the constitutional documents of the Guarantor as in effect after the Re-domestication, certified as being true and correct by an officer of the Guarantor; and (b) an opinion letter of Swiss counsel to the Guarantor substantially in the form of Exhibit A (and the Guarantor acknowledges and agrees that failure to timely deliver such items shall constitute an Event of Default).

SECTION 6. Designation as a Finance Document. The Obligors and the Agent agree that this Amendment is a Finance Document.

SECTION 7. Continuing Effectiveness, etc. Each Obligor affirms that after giving effect to the Re-domestication and the effectiveness of this Amendment, the Credit Agreement, as amended hereby, and each other Finance Document to which such Obligor is a party will remain in full force and effect and will continue to constitute a legal, valid and binding obligation of such Obligor, enforceable against such Obligor in accordance with its terms. Without limiting the

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foregoing, the Guarantor represents and warrants that (a) the Re-domestication will not interrupt the continued corporate existence of the Guarantor and (b) all of the assets, property, rights, liabilities and obligations of the Guarantor immediately prior to the Re-domestication (including all rights, liabilities and obligations of the Guarantor under the Finance Documents) will continue to be the assets, property, rights, liabilities and obligations of the Guarantor after the Re-domestication.

SECTION 8. Miscellaneous.

8.1 Effect of Amendment. After the effectiveness hereof, all references to the Credit Agreement set forth in any other agreement or instrument shall, unless otherwise specifically provided, be references to the Credit Agreement as amended hereby. Except as so amended, the Credit Agreement and the other Finance Documents shall remain in full force and effect in accordance with their respective terms. The Obligors agree that the waiver described in Section 2 is limited to the specific terms thereof and shall not constitute or be deemed a waiver of any other Default or of any right or remedy arising as a result of any such other Default.

8.2 Incorporation of Certain Provisions. Clauses 1.2 (Interpretation), 1.5 (Headings), 1.8 (Third Party Rights), 29.1 (Binding Agreement), 32 (Remedies and Waivers, Partial Invalidity), 36 (Governing Law) and 37 (Jurisdiction) of the Credit Agreement shall apply hereto as if fully set forth herein, mutatis mutandis (it being understood that references therein to “this Agreement” or “the Finance Documents” are references to this Amendment).

8.3 Counterparts. This Amendment may be executed in any number of counterparts and by different parties hereto on separate counterparts, each of which shall be an original and all of which taken together shall constitute one and the same agreement. Delivery to the Agent of a signed counterpart hereof, or signature page hereto, by facsimile or e-mail (in a .pdf or similar file) shall be effective as delivery of an original manually-signed counterpart.

8.4 Further Assurances. Each Obligor shall, at the request of the Agent and at its own expense, do all such acts and things necessary or desirable to give effect to the amendments effected or to be effected pursuant to this Amendment.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed by their duly authorized officers as of the date first above written.

Signature Page to Third Amendment to

ACE A$ Credit Agreement

ACE AUSTRALIA HOLDINGS PTY LIMITED

Signature Page to Third Amendment to

ACE A$ Credit Agreement

Signature Page to Third Amendment to

ACE A$ Credit Agreement