AXIS SPECIALTY FINANCE LLC 5.875% Senior Notes Due June 1, 2020

Exhibit 4.1

[THIS NOTE IS A GLOBAL SECURITY WITHIN THE MEANING OF THE INDENTURE HEREINAFTER REFERRED TO, UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY (“DTC”), A NEW YORK CORPORATION, TO AXIS SPECIALTY FINANCE LLC OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

UNLESS AND UNTIL IT IS EXCHANGED IN WHOLE OR IN PART FOR SECURITIES IN DEFINITIVE FORM, THIS SECURITY MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO THE NOMINEE OF THE DEPOSITARY OR BY A NOMINEE OF THE DEPOSITARY TO THE DEPOSITARY OR ANOTHER NOMINEE OF THE DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A SUCCESSOR DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITARY.]

AXIS SPECIALTY FINANCE LLC

5.875% Senior Notes

Due June 1, 2020

Fully and unconditionally

guaranteed by

AXIS CAPITAL HOLDINGS LIMITED

AXIS Specialty Finance LLC, a limited liability company organized under the laws of Delaware (the “Issuer,” which term includes any successor corporation under the Indenture referred to on the reverse hereof), for value received, hereby promises to pay to CEDE & CO., or registered assigns, the principal sum of [            ] DOLLARS on the Stated Maturity shown above, and to pay interest thereon from the Original Issue Date shown above, or from the most recent Interest Payment Date to which interest has been paid or duly provided for, semi-annually in arrears on each Interest Payment Date as specified above, commencing on [            ], and on the Stated Maturity at the rate per year shown above until the principal hereof is paid or made available for payment and on any overdue principal and on any overdue installment of interest to the extent permitted by law. The interest so payable, and punctually paid or duly provided for, on any Interest Payment Date (other than an Interest Payment Date that is the Stated Maturity or a Redemption Date) will, as provided in the Indenture, be paid to the Person in whose name this Note is registered at the close of business on the Regular Record Date as specified above next preceding such Interest Payment Date, provided that any interest payable at Stated Maturity or on a Redemption Date will be paid to the Person to whom principal is payable. Except as otherwise provided in the Indenture, any such interest that is not so punctually paid or duly provided for will forthwith cease to be payable to the Holders on such Regular Record Date and may be paid as provided in Section 2.7 of the Indenture.

Payments of interest on this Note will include interest accrued to but excluding the respective Interest Payment Dates. Interest payments for this Note shall be computed and paid on the basis of a 360-day year consisting of twelve 30-day months. In the event that any date on which interest is payable on this Note is not a Business Day, then payment of the interest payable on such date will be made on the next succeeding day that is a Business Day (and without any interest or other payment in respect of any such delay), except that, if such Business Day is in the next succeeding calendar year, payment shall be made on the immediately preceding Business Day, in each case with the same force and effect as if made on the date the payment was originally payable.

Payment of the principal of and interest due at the Stated Maturity or a Redemption Date of this Note shall be made upon surrender of this Note at the Corporate Trust Office of the Trustee. The principal of and interest on this Note shall be paid in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts. Payment of interest (including interest on an Interest Payment Date) will be made, subject to such surrender where applicable, at the option of the Issuer, (i) by check mailed to the address of the Person entitled thereto as such address shall appear in the Security Register or (ii) by wire transfer at such place and to such account at a banking institution in the United States as may be designated in writing to the Trustee at least 15 days prior to the date for payment by the Person entitled thereto.

The Senior Notes (as defined on the reverse hereof will be unsecured obligations of the Issuer and will rank equally in right of payment with all other unsecured, senior indebtedness of the Issuer from time to time outstanding. The Senior Notes will rank senior to any subordinated indebtedness of the Issuer.

AXIS Capital Holdings Limited (the “Guarantor”) does hereby fully and unconditionally guarantee (the “Guarantee”) to the Holders and to the Trustee all payment obligations of the Issuer on this Note when due, in accordance with the provisions of this Indenture, as provided below. The Guarantee shall rank equally in right of payment with other unsecured, senior indebtedness of the Guarantor. The Guarantee will rank senior to any subordinated indebtedness of the Guarantor.

REFERENCE IS HEREBY MADE TO THE FURTHER PROVISIONS OF THIS NOTE SET FORTH ON THE REVERSE HEREOF, WHICH FURTHER PROVISIONS SHALL FOR ALL PURPOSES HAVE THE SAME EFFECT AS IF SET FORTH AT THIS PLACE.

Unless the certificate of authentication hereon has been executed by the Trustee by manual signature, this Note shall not be entitled to any benefit under the Indenture or be valid or obligatory for any purpose.

IN WITNESS WHEREOF, the Issuer has caused this instrument to be duly executed.

CERTIFICATE OF AUTHENTICATION

This is one of the 5.875% Senior Notes due 2020 referred to in the within-mentioned Indenture.

(Reverse Side of Note)

This Note is one of a duly authorized issue of Senior Notes of the Issuer issued and issuable in one or more series under a Senior Indenture dated as of March 23, 2010 (the “Indenture”), among the Issuer, the Guarantor and The Bank of New York Mellon Trust Company, N.A., as Trustee (the “Trustee,” which term includes any successor trustee under the Indenture), to which Indenture and all indentures incidental thereto reference is hereby made for a statement of the respective rights, limitations of rights, duties and immunities thereunder of the Issuer, the Guarantor, the Trustee and the Holders of the Senior Notes issued thereunder and of the terms upon which said Senior Notes are, and are to be, authenticated and delivered. This Note is one of the series designated on the face hereof as 5.875% Senior Notes due 2020 (the “Senior Notes”), initially limited in aggregate principal amount of $500,000,000; provided, however, that the aggregate principal amount of the Senior Notes may be increased in the future, without the consent of the holders of the Senior Notes, on the same terms and with the same CUSIP and ISIN numbers as the Senior Notes. Capitalized terms used herein for which no definition is provided herein shall have the meanings set forth in the Indenture.

This Note is exchangeable in whole or from time to time in part for Senior Notes of this series in definitive registered form only as provided herein and in the Indenture. If (i) at any time the Depositary notifies the Issuer that it is unwilling or unable to continue as Depositary for this Note, and the Issuer does not appoint a successor Depositary within 90 days after the Issuer receives such notice or becomes aware of such condition, as the case may be, (ii) at any time, the Depositary ceases to be a clearing agency registered under the Securities Exchange Act of 1934 and the Issuer has not appointed a successor depositary within 90 days after the Issuer learns that the Depositary has ceased to be so registered or (iii) the Issuer in its sole discretion determines that this Note shall be exchangeable for Senior Notes of this series in definitive registered form and executes and delivers to the Security Registrar a written order of the Issuer providing that this Note shall be so exchangeable, this Note shall be exchangeable for Senior Notes of this series in definitive registered form, provided that the definitive Senior Notes so issued in exchange for this Note shall be in denominations of $2,000 and whole multiples of $1,000 in excess of $2,000, without coupons, and be of like aggregate principal amount and tenor as the portion of this Note to be exchanged. Except as provided above, owners of beneficial interests in this Note will not be entitled to have Senior Notes registered in their names, will not receive or be entitled to physical delivery of Senior Notes in definitive registered form and will not be considered the holders thereof for any purpose under the Indenture. Neither the Issuer, the Guarantor, the Trustee, any Paying Agent nor the Security Registrar shall have any responsibility or liability for any aspect of records relating to or payments made on account of beneficial ownership interests in this Note, or for maintaining, supervising or reviewing any records relating to such beneficial ownership interests.

If an Event of Default with respect to the Senior Notes shall occur and be continuing, the principal of the Senior Notes may become or may be declared due and payable in the manner, with the effect and subject to the conditions provided in the Indenture.

The Indenture permits, with certain exceptions as therein provided, the amendment thereof and the modification of the rights and obligations of the Issuer and the rights of the Holders of the Senior Notes under the Indenture at any time by the Issuer and the Trustee with the consent of the Holders of not less than a majority in aggregate principal amount of the Senior Notes at the time Outstanding. The Indenture also contains provisions permitting the holders of specified percentages in principal amount of the Senior Notes at the time Outstanding, on behalf of the holders of all Senior Notes, to waive compliance by the Issuer with certain provisions of the Indenture and certain past defaults under the Indenture and their consequences. Any such consent or waiver by the Holder of this Note shall be conclusive and binding upon such holder and upon all future Holders of this Note and of any Senior Note issued upon the registration of transfer hereof or in exchange hereof or in lieu hereof, whether or not notation of such consent or waiver is made upon this Note.

The Indenture contains provisions for defeasance at any time of (a) the entire indebtedness of the Issuer pursuant to this Note and (b) restrictive covenants and the related Events of Default, upon compliance by the Issuer with certain conditions set forth therein, which provisions apply to this Note.

The Senior Notes will be redeemable, at the option of the Issuer, in whole or in part, at any time (a “Redemption Date”), at a redemption price (the “Redemption Price”) equal to the greater of (i) 100% of the aggregate principal amount of the Senior Notes to be redeemed and (ii) an amount equal to the sum of the present values of the remaining scheduled payments for principal and interest on the Senior Notes to be redeemed, not including any portion of the payments of interest accrued as of such Redemption Date, discounted to such Redemption Date on a semi-annual basis (assuming a 360-day year consisting of twelve 30-day months) at the Treasury Rate, plus 35 basis points; plus in each case, accrued and unpaid interest on the principal amount being redeemed to, but excluding, such Redemption Date.

“Treasury Rate” means (1) the yield, under the heading which represents the average for the immediately preceding week, appearing in the most recently published statistical release designated “H.15(519)” or any successor publication which is published weekly by the Board of Governors of the Federal Reserve System and which establishes yields on actively traded United States Treasury securities adjusted to constant maturity under the caption “Treasury Constant Maturities,” for the maturity corresponding to the Comparable Treasury Issue (if maturity is within three months before or after the remaining life, yields for the two published maturities most closely corresponding to the Comparable Treasury Issue will be determined and the Treasury Rate will be interpolated or extrapolated from such yields on a straight line basis, rounding to the nearest month), or (2) if such release (or any successor release) is not published during the week preceding the calculation date or does not contain such yields, the rate per year equal to the semi-annual equivalent yield to maturity of the Comparable Treasury Issue, calculated using a price for the Comparable Treasury Issue (expressed as a percentage of its principal amount) equal to the Comparable Treasury Price for such Redemption Date. The Treasury Rate shall be calculated on the third Business Day preceding the Redemption Date.

“Comparable Treasury Issue” means the United States Treasury security selected by the Independent Investment Banker as having a maturity comparable to the remaining term of the Senior Notes to be redeemed.

“Independent Investment Banker” means Barclays Capital Inc., Deutsche Bank Securities Inc., Wells Fargo Securities, LLC and their successors or, if none of such firms is willing or able to select the Comparable Treasury Issue, an independent investment banking institution of national standing appointed by the Trustee after consultation with the Issuer.

“Comparable Treasury Price” means (1) the average of four Reference Treasury Dealer Quotations for such Redemption Date, after excluding the highest and lowest of such Reference Treasury Dealer Quotations, or (2) if the trustee obtains fewer than four such Reference Treasury Dealer Quotations, the average of all such quotations.

“Reference Treasury Dealer” means each of Barclays Capital Inc., Deutsche Bank Securities Inc., Wells Fargo Securities, LLC and their respective successors and one other primary U.S. government securities dealer (each a “Primary Treasury Dealer”), as specified by the Issuer; provided, that (1) if any of the foregoing shall cease to be a Primary Treasury Dealer, the Issuer will substitute therefor another Primary Treasury Dealer and (2) if the Issuer fails to select a substitute within a reasonable period of time, then the substitute will be a Primary Treasury Dealer selected by the Independent Investment Banker after consultation with the Issuer.

“Reference Treasury Dealer Quotations” mean, with respect to the Reference Treasury Dealer and any Redemption Date, the average, as determined by the Independent Investment Banker, of the bid and asked prices for the Comparable Treasury Issue (expressed, in each case, as a percentage of its principal amount) quoted in writing to the Independent Investment Banker by such Reference Treasury Dealer at 5:00 p.m., New York City time, on the third Business Day preceding such Redemption Date.

Notice of any redemption will be mailed at least 30 days but no more than 60 days before the Redemption Date to each Holder of the Senior Notes to be redeemed. Notwithstanding Section 12.2 of the Indenture, the notice of redemption with respect to the foregoing redemption need not set forth the Redemption Price but only the manner of calculation thereof.

The Issuer shall notify the Trustee of the Redemption Price with respect to the foregoing redemption promptly after the calculation thereof. The Trustee shall not be responsible for calculating said Redemption Price. Unless the Issuer defaults in payment of the redemption price, on and after the redemption date, interest will cease to accrue on the Senior Notes or portions thereof called for redemption.

If less than all of the Senior Notes are to be redeemed, the Trustee shall select, in such manner as it deems appropriate and fair, the principal amount of such Senior Notes held by each beneficial owner of such Senior Notes to be redeemed. The

Trustee may select notes and portions of notes in amounts of $2,000 and whole multiples of $1,000 in excess of $2,000.

No reference herein to the Indenture and no provision of this Note or of the Indenture shall alter or impair the obligation of the Issuer, which is absolute and unconditional, to pay the principal of and interest on this Note at the time, place and rate, and in the coin or currency, herein prescribed.

As provided in the Indenture and subject to certain limitations therein set forth, the transfer of this Note is registrable in the Security Registration surrender of this Note for registration of transfer at the office or agency of the Issuer for such purpose, duly endorsed by, or accompanied by a written instrument of transfer in form satisfactory to the Issuer or the Security Registrar and duly executed by, the Holder hereof or his/her attorney duly authorized in writing, and thereupon one or more new Senior Notes, of authorized denominations and of like tenor and for the same aggregate principal amount, will be issued to the designated transferee or transferees. No service charge shall be made for any such exchange or registration of transfer, but the Issuer will require payment of a sum sufficient to cover any tax or other governmental charge payable in connection therewith.

Prior to due presentment of this Note for registration of transfer, the Issuer, the Trustee, any Person authorized by the Issuer to pay the principal of or any premium or interest on any Securities on behalf of the Issuer (“Paying Agent”) and the Security Registrar of the Issuer or the Trustee may deem and treat the Person in whose name this Note is registered as the absolute owner hereof for all purposes, whether or not this Note be overdue and notwithstanding any notice of ownership or writing thereon made by anyone other than the Security Registrar, and neither the Issuer nor the Trustee nor any Paying Agent nor the Security Registrar shall be affected by notice to the contrary.

The Senior Notes are issuable only in registered form without coupons in denominations of $2,000 and whole multiples of $1,000 in excess of $2,000. As provided in the Indenture and subject to certain limitations therein set forth, Senior Notes are exchangeable for a like aggregate principal amount of Senior Notes of a different authorized denomination, as requested by the Holder surrendering the same upon surrender of the Senior Note or Senior Notes to be exchanged at the office or agency of the Issuer.

No recourse shall be had for payment of the principal of or interest on this Note, or for any claim based hereon, or otherwise in respect hereof, or based on or in respect of the Indenture, against any incorporator, as such or against any past, present or future shareholder, officer or director, as such, of the Issuer or of any successor, either directly or through the Issuer or any successor, under any rule, law, statute or constitutional provision, or by the enforcement of any assessment or by any legal or equitable proceeding or otherwise, all such liability being expressly waived and released, by the acceptance hereof and as part of the consideration for the issuance hereof.

Unless the certificate of authentication hereon has been executed by the Trustee by manual signature, this Note shall not be entitled to any benefit under the Indenture or be valid or obligatory for any purpose.

This Note shall be deemed to be a contract under the laws of the State of New York, and for all purposes shall be construed in accordance with the laws of such state, except as may be required by mandatory provisions of law.

ABBREVIATIONS

The following abbreviations, when used in the inscription on the face of this instrument, shall be construed as though they were written out in full according to applicable laws or regulations:

Additional abbreviations may also be used

though not on the above list.

FOR VALUE RECEIVED, the undersigned hereby sell(s) and transfer(s) unto

PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING POSTAL ZIP CODE OF ASSIGNEE

(please insert Social Security or other identifying number of assignee)

the within Note and all rights thereunder, hereby irrevocably constituting and appointing

agent to transfer said Note on the books of the Issuer, with full power of substitution in the premises.