Exhibit 99.1

May 24, 2006

Board of Directors
Stone Energy Corporation
625 E. Kaliste Saloom Road
Lafayette, LA 70508

Attention: James H. Stone
Chairman of the Board

     Dear Jimmy:

     We are pleased to submit this offer to combine the businesses of our two companies, subject to the terms and conditions discussed below. Our offer clearly meets the standard for a Target Superior Proposal as contemplated by your merger agreement with Plains.

     We propose to acquire all the shares of Stone for a combination of cash and stock at a price of $52.00 per Stone share, subject to a limit on the number of EPL shares to be issued. Under the terms of our offer, each Stone share will be exchanged for $26.00 in cash and a variable number of shares of EPL common stock having a value of $26.00 based on the average closing price over the 20 trading days preceding the closing of the merger, provided that the number of EPL shares to be issued for each Stone share will range from a maximum of 1.287 to a minimum of 1.053, based on our assumption of 27.7 million fully diluted Stone shares. Based on our closing price today, that would equate to 1.21 EPL shares for each Stone share. We will provide the opportunity for each Stone shareholder to elect whether to receive the consideration in cash or common stock of EPL, subject to the limitation that the total value of the cash consideration payable for the shares will be approximately $720 million. We intend to structure the transaction so that receipt of our shares would be tax free to your shareholders who elect to receive shares.

     We call your attention to the following:

• Our offer ($52.00 per Stone share) represents a 26.21% premium over the current value of the Plains offer ($41.20 per Stone
share based on today’s closing price for Plains’ shares).

• Our offer represents aggregate additional consideration of approximately $300 million to Stone’s shareholders.

• Fully 50% of our offer is in cash, which combined with our variable exchange ratio (subject to a collar), will substantially protect the offer value from changes in EPL’s share price.

• Given the overlapping nature of a significant portion of our asset base, we believe there are material overhead and operating cost savings that will create additional value for Stone’s shareholders who continue as EPL shareholders.

     Our offer is not subject to any financing contingency. We have received a commitment letter from Bank of America, N.A. and affiliates
for the financing necessary to consummate the proposed transaction.

     We have carefully reviewed all information filed by Stone with the SEC, and believe that we can complete our due diligence review of your Company promptly. We are available to commence our due diligence review immediately, and we are confident that, assuming full cooperation, we can complete our review within 7 to 10 days. We are also prepared to give you and your representatives full access to our non-public information for purposes of your due diligence review of us.

     Our board of directors has approved the submission of our offer. Any definitive transaction between EPL and Stone would, of course, be subject to final approval by our board and our shareholders. We are prepared to enter into a merger agreement reflecting the above terms and which would otherwise be substantially similar to the merger agreement that you entered into with Plains. We believe that the proposed transaction could close in the third quarter of 2006.

     This letter is not intended to, and does not, create or constitute any legally binding obligation, liability or commitment by us regarding the proposed transaction, and, other than the confidentiality agreement we will enter into with you, there will be no legally binding contract or agreement between us regarding the proposed transaction unless and until a definitive merger agreement is executed.

     We and our financial advisors, Evercore Group L.L.C. and Banc of America Securities LLC, and our legal advisors, Cahill Gordon & Reindel LLP, are prepared to move forward immediately with our offer. We believe that it presents a compelling opportunity for both our companies, and look forward to your prompt response.

Very truly yours,

/s/ Richard A. Bachmann

Richard A. Bachmann
Chairman of the Board and Chief Executive Officer

cc:  David H. Welch, President and Chief Executive Officer, Stone Energy Corporation