NINTH AMENDMENT AGREEMENT

Exhibit 10.5

EXECUTION COPY

NINTH AMENDMENT AGREEMENT

THIS NINTH AMENDMENT AGREEMENT dated as of 10 July, 2008 (this “Amendment Agreement”) amends the Letter of Credit Facility Agreement originally dated as of 19 November, 1999 (as most recently amended pursuant to the Seventh Amendment and Restatement Agreement dated 17 November, 2006 and the Eighth Amendment Agreement dated as of 16 November, 2007, the “Facility Agreement”) between, among others, ACE Limited (the “Account Party”), certain subsidiaries thereof, as guarantors, various banks and Citibank International plc, as agent and security trustee for the banks. Capitalized terms used but not defined herein have the respective meanings set forth in the Facility Agreement, and the principles of construction set forth in the Facility Agreement shall apply to this Amendment Agreement as if set forth in full herein.

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

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

NOW, THEREFORE, the parties hereto agree as follows:

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

1.1 The first sentence of Clause 16.1 (Corporate Existence and Power) is amended by (a) substituting the phrase “a company limited by shares” therein for the phrase “a share corporation (Aktiengesellschaft)” and (b) substituting the reference to “the Cayman Islands” therein for the phrase “its jurisdiction of incorporation, formation or organization”.

1.2 Clause 17.7 (Inspection of Property, Books and Records) is amended by adding the phrase “or if such disclosure would violate any applicable law” before the period at the end thereof.

1.3 The following Clause 17.16 is added in appropriate numerical sequence:

The Obligors shall ensure that (a) neither the Charged Portfolio nor any account comprising the Charged Portfolio is held or maintained in Switzerland and (b) the Custodian is not organised under the laws of Switzerland.

1.4 Clause 18.7.1 (Winding-up of the Account Party or a Guarantor) is amended by substituting the reference to “the Grand Court of the Cayman Islands” therein for the phrase “a court or authority of competent jurisdiction in any relevant jurisdiction”.

1.5 Clause 33.6 (Deemed receipt by the Obligors) is amended by substituting the words “all Obligors” for “both Obligors” immediately before the period at the end thereof.

SECTION 2. Waiver. The Majority Banks waive any Default that may arise under Clause 17.5 (Conduct of Business and Maintenance of Existence) of the Facility Agreement upon completion of the re-domestication of the Account Party 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 Agreement 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 Agreement 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 Agreement: (a) each representation and warranty of such Obligor contained in Clause 16 of the Facility 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 Agreement. This Amendment Agreement (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 amendments 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 Account Party 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 Account Party as in effect after the Re-domestication, certified as being true and correct by an officer of the Account Party; and (b) an opinion letter of Swiss counsel to the Account Party substantially in the form of Exhibit A (and the Account Party acknowledges and agrees that failure to timely deliver such items shall constitute an Event of Default).

SECTION 6. Designation as a Finance Document. The Account Party and the Agent agree that this Amendment Agreement 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 Agreement, the Facility

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

SECTION 8. Miscellaneous.

8.1 Effect of Amendment Agreement. After the effectiveness hereof, all references to the Facility Agreement set forth in any other agreement or instrument shall, unless otherwise specifically provided, be references to the Facility Agreement as amended hereby. Except as so amended, the Facility 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 Event of Default or of any right or remedy arising as a result of any such other Default or Event of Default.

8.2 Governing Law. This Amendment Agreement shall be governed by and construed in accordance with English law.

8.3 Successors and Assigns. This Amendment Agreement shall be binding upon, inure to the benefit of and be enforceable by the respective successors and assigns of the parties hereto.

8.4 Construction. Headings used herein are for convenience of reference only and shall not affect the meaning of this Amendment Agreement.

8.5 Incorporation of Certain Provisions. Clauses 1.8 (Third party Rights), 32 (Remedies and Waivers, Partial Invalidity) and 37 (Jurisdiction) of the Facility 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 Agreement).

8.6 Counterparts. This Amendment Agreement 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.

8.7 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 Agreement.

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

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