AMENDMENT NO. 1 TO THE RESTRICTED UNIT AWARD AGREEMENT

Exhibit 10.56

AMENDMENT NO. 1 TO THE RESTRICTED UNIT AWARD AGREEMENT

THIS AMENDMENT NO. 1 TO THE RESTRICTED UNIT AWARD GRANT AGREEMENT (the “Amendment”), made as of this 8th day of December 2009 between Polymer Holdings LLC (the “Company”) and David A. Bradley (the “Participant”).

WHEREAS, Kraton Polymers LLC (“Kraton Polymers”) and the Participant entered into a restricted unit award grant agreement, dated as of June 19, 2008 (the “Agreement”) pursuant to which Kraton Polymers granted a Restricted Unit Award to the Participant;

WHEREAS, as a result of the structural changes of the Company and its affiliates, including the initial public offering of the Company and the merger of TJ Chemical Holdings LLC (“TJ Chemical”) into Kraton Polymers (together, the “Transactions”), the Company wishes to assume the rights and obligations of Kraton Polymers, TJ Chemical and its affiliates with respect to the outstanding Restricted Unit Awards;

WHEREAS, as a result of the Transactions, it is anticipated that each holder of Membership Units of TJ Chemical will receive one common share of the Company for every 13.512 Membership Units (or such other number of Membership Units that is ultimately required to receive one common share of the Company by holders of Membership Units as of the effective date of the initial public offering of the Company) (1 divided by such number of Membership Units, the “Conversion Ratio”); and

WHEREAS, the compensation committee of the Company has determined to make, and the board of directors of the Company has approved, appropriate adjustments to the Restricted Unit Award;

NOW, THEREFORE, in consideration of the mutual covenants and promises contained herein and for other good and valuable consideration, the Company and the Participant hereby agree that, effective as of the date hereof, the Agreement is hereby amended as follows:

1. Conversion. As of the date hereof, 100,000 of the Restricted Units granted to the Participant pursuant to the Agreement are vested and currently held by the Participant as Membership Units. These Membership Units shall not be affected by this Amendment. The unvested portion Restricted Unit Awards will be converted from 200,000 Restricted Units into shares of restricted stock of the Company equal to the product of (i) 200,000 and (ii) the Conversion Ratio (the “Restricted Shares”), subject to the terms and conditions of such Restricted Shares as set forth herein.

2. Effectiveness of Certain Provisions. Section 4 of the Agreement (entitled “Limitation on Transfer of Membership Units; Permissible Assignments; Termination of Employment”) and all references to the “Operating Agreement” in the Agreement (including, without limitation, in Sections 7.1(a), 8 and 11) shall cease to be of any force or effect.

3. Other Terms and Conditions. Except as expressly provided for in this Amendment, the Restricted Shares shall continue to be subject to the same terms and conditions set forth in the

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Agreement, including, without limitation, the vesting schedule set forth therein; provided that, all references in the Agreement to (i) “TJ Chemical” or “Management LLC” shall be deemed to refer to the Company, (ii) “Restricted Units” shall be deemed to refer to Restricted Shares, and (iii) a “membership unit” of an entity shall be deemed to refer to a Share.

4. Integration. Except as otherwise specifically provided in this Amendment, all terms and conditions of the Agreement shall remain in full force and effect.

5. Counterparts. This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which shall constitute one and the same instrument.

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IN WITNESS WHEREOF, the Company has caused this Amendment to be duly executed by its duly authorized officer and said Participant has hereunto signed this Amendment on his own behalf, thereby representing that he has carefully read and understands this Amendment as of the day and year first written above.

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