CONSULTING SERVICES AGREEMENT

Exhibit 10.1

CONSULTING SERVICES AGREEMENT

THIS CONSULTING SERVICES AGREEMENT (“Agreement”) is made and entered into, as of the effective date set forth on the signature page hereof, by and between GTS Consulting, LLC (“GTS”) and ACE American Insurance Company, a Pennsylvania corporation (“ACE”).

WHEREAS, Gary Schmalzriedt (“Executive”) is presently employed as Chairman of ACE Overseas General; and

WHEREAS, the Executive will retire from ACE effective September 30, 2006; and

WHEREAS, ACE considers it essential to obtain the benefit of the Executive’s experience as an executive officer of ACE during the period immediately following the Executive’s termination of employment;

WHEREAS, to induce GTS to execute this Agreement for Executive’s services as a consultant, the parties desire to enter into a written Consulting Services Agreement;

NOW, THEREFORE, in consideration of the mutual promises set forth herein, and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereby agree as follows:

1. Termination of Employment. Executive will retire from ACE effective September 30, 2006.

2. Independent Contractor. From October 1, 2006 until September 30, 2007, ACE shall retain GTS as an independent contractor, and nothing herein shall be construed or deemed as creating any other relationship during that time. From October 1, 2006 until September 30, 2007, Executive shall not hold the title of Chairman ACE Overseas General and shall not have the authority of that officer position to act on behalf of ACE.

3. Consulting Services. From October 1, 2006 to September 30, 2007, GTS hereby agrees to provide and perform for the benefit of ACE the duties and responsibilities described below and in addition those as may be prescribed from time to time by the Board of Directors of ACE Limited and/or the Chief Executive Officer of ACE Limited (“Consulting Services”). GTS shall ensure that Executive shall devote such time and attention to the Consulting Services as may be necessary or required to complete such Consulting Services. Executive shall be permitted to travel at the request of ACE management in the performance of the Consulting Services in accordance with the ACE Executive Travel Policy. Executive shall be entitled to fly business class for all business travel on airplanes.

For the term of the Agreement, GTS through Executive will, as requested by ACE and agreed to by GTS, such agreement not to be unreasonably withheld, provide services to Employer which

relate to matters for which Executive was responsible in connection with his former position with Employer or which relate to the establishment and operation of a training program known as a “War College.” Executive will serve as Dean of the War College and in such role, will design the curriculum, solicit instructors and be responsible for delivery of the program. Upon reasonable advanced notice, Executive will make himself available during the term of this Agreement to provide Consulting Services for periods of time as reasonably required by Employer and will report to Evan Greenberg concerning the provision of Consulting Services.

4. Termination of this Agreement. ACE may terminate this Agreement with or without cause at ACE’s discretion and convenience at any time prior to September 30, 2007 by giving the Executive thirty (30) days prior written notice. In addition, ACE may terminate this Agreement immediately for cause, which shall include the failure to perform the Consulting Services, without prior written notice and such termination shall be effective immediately upon notice to the Executive. In the event that this Agreement is terminated for cause, all consideration described in paragraph 5 below shall cease as of the date this Agreement is terminated. “Cause” shall mean embezzlement of ACE funds, habitual insobriety or drug abuse during business hours or while performing the Consulting Services, conviction of a crime involving moral turpitude, or gross negligence in the performance of the Executive’s Consulting Services which gross negligence has had a material adverse effect on the consolidated business, assets, properties or financial condition of ACE or its affiliates. If the Agreement is terminated without cause, Executive will still receive the consideration set forth in paragraphs 5(a), (b) and (c) below.

5. Consideration. As consideration for the GTS’s performance of the Consulting Services from October 1, 2006 through September 30, 2007, ACE shall compensate the Executive as follows:

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(i) Executive will incur a tax liability for the restricted shares of ACE Limited stock as said shares vest, and

(ii) continued vesting in the restricted shares is expressly conditioned on Executive continuing to perform Consulting Services under this Agreement to the satisfaction of Employer during the term of the Agreement.

6. Confidential Information. The GTS and Executive recognize and acknowledge that while employed by ACE, the Executive had access to, has learned and been provided with, and has prepared and created, certain confidential and proprietary business information and trade secrets for ACE; and, further, the Executive hereby acknowledges and agrees that all corporate records and other confidential information not released to the public, all trade secrets and all other confidential or proprietary information of ACE, in each case relating to the business and operations of ACE, are confidential and the sole property of ACE (collectively referred to as “Confidential Information”). The Executive and GTS acknowledge that, in their performance of the Consulting Services, they may become privy to Confidential Information. GTS and Executive agree not to use or disclose any Confidential Information except in the regular or normal course of the their performance of the Consulting Services. On September 30, 2007, or upon the termination of this Agreement, if earlier, the GTS and Executive will surrender to ACE all written Confidential Information in their possession. Further, GTS and Executive agree that, on September 30, 2007, or upon the termination of this Agreement, if earlier, not to use or cause to be used for the Executive’s own benefit or for the benefit of any third parties, or to disclose to any third party, in any manner, directly or indirectly, any Confidential Information.

7. Indemnification. ACE shall indemnify and hold harmless the Executive against any claims, causes of action, liabilities, debts, and judgments, as well as any and all reasonable costs and expenses, including reasonable attorneys’ fees, that may be incurred by the Executive in any threatened, pending, or completed action, suit, or proceeding, whether civil, criminal, or administrative, or investigative and whether formal or informal, because of the Executive’s performance of the Consulting Services described in this Agreement, unless and to the extent determined to be caused by the Executive’s gross negligence or willful misconduct.

8. Covenant Not to Compete. From October 1, 2006 until September 30, 2007, GTS and the Executive shall not, without the prior written consent of ACE, directly or indirectly, own,

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manage or operate or participate in the ownership, management or operation of, or be connected as an officer, director, employee, partner or shareholder with, any business entity which competes with or which is engaged in activities in competition with those activities conducted by ACE or any of its parents, subsidiaries or affiliates, within the geographic territory served by ACE; provided, however, that ownership of five percent (5%) or less of a class of outstanding securities of or other ownership interests in such a business entity shall not constitute a breach or violation of the foregoing covenant. In the event that the provisions of this paragraph 8 should ever be deemed to exceed the time or geographic limitations permitted by applicable law, then such provisions shall be deemed reformed to the maximum permissible time of geographic limitations.

9. No Right to Employment. Nothing in this Agreement shall create any right in the Executive to employment with ACE or any affiliate of ACE.

10. Severability and Survival. In the event any provision of this Agreement shall be determined to be invalid, the remainder of this Agreement shall continue in full force and effect. The duties and obligations of GTS and the Exeuctive set forth herein with respect to ACE’s Confidential Information, and the provisions hereof relating to such duties and obligations, shall survive indefinitely completion of the Consulting Services and the termination of this Agreement for any reason.

11. Captions. Captions contained in this Agreement are inserted for convenience only and in no way define, limit or extend the scope of intent of any provision of this Agreement.

12. Arbitration and Applicable Law. GTS, Executive and ACE agree that any disagreements, disputes, or claims arising out of or relating to the validity of this Agreement or how it is interpreted or implemented and those involving in any way, or related to Executive’s employment with ACE or the termination of that employment, shall be resolved exclusively by arbitration in Philadelphia, Pennsylvania, in accordance with the Employment Dispute Resolution Rules of the American Arbitration Association and judgment upon the award rendered by the Arbitrator may be entered in any court having jurisdiction over the matter. The terms and conditions of this Agreement shall be construed and enforced according to the laws of the Commonwealth of Pennsylvania, without regard to Pennsylvania conflicts of laws principles.

13. Assignment. This is a contract for the personal services of the Executive. GTS may not assign this Agreement or delegate Executive’s duties hereunder without the prior written consent of ACE and any attempted assignment or delegation shall be of no force or effect.

14. Entire Agreement; Amendments. There are no representations, agreements, arrangements, or understandings, oral or written, as to the Consulting Services to be performed and provided under this Agreement except as expressed herein. This Agreement may not be amended except in a writing signed by both parties hereto.

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15. Notice. Any written notice under this Agreement shall be personally delivered to the other party or sent by certified or registered mail, return receipt requested and postage prepaid, to ACE at 436 Walnut Street, Philadelphia, Pa. 19106, c/o Phillip Cole and to the Executive at the most recent home address of which he has informed ACE, or, as to either party, to such other address as either party may from time to time specify by written notice.

IN WITNESS WHEREOF, the parties have executed this Agreement intending to be legally bound as of the effective date set forth below.

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