Exhibit 99.1

CONTACT:

R. Dirk Allison

Senior Vice President and Chief Financial Officer

(214) 922-9711

ODYSSEY HEALTHCARE EXPECTS SECOND QUARTER DILUTED EPS

ATTRIBUTABLE TO ODYSSEY STOCKHOLDERS OF $0.39 TO $0.41

DALLAS, TEXAS (July 19, 2010) — Odyssey HealthCare, Inc. (NASDAQ: ODSY), one of the largest providers of hospice care in the United States, today announced that it expects to report fully diluted earnings per share attributable to Odyssey stockholders of $0.39 to $0.41 for the second quarter ended June 30, 2010. The Company expects to report full results on July 28, 2010; however, due to its previously announced acquisition by Gentiva Health Services, Inc. (NASDAQ: GTIV), the Company will not be hosting a conference call in connection with second quarter results.

The Company also announced that, during the second quarter, it redeemed at par the remaining $13 million of auction rate securities held by the Company.

Based in Dallas, Texas, Odyssey is one of the largest providers of hospice care in the country in terms of both average daily patient census and number of locations. Odyssey seeks to improve the quality of life of terminally ill patients and their families by providing care directed at managing pain and other discomforting symptoms and by addressing the psychosocial and spiritual needs of patients and their families.

Additional Information

Odyssey HealthCare, Inc. (the “Company”) filed a definitive proxy statement with the Securities and Exchange Commission (the “SEC”) on July 9, 2010 and intends to file other relevant materials in connection with the acquisition in due course. The definitive proxy statement has been sent or given to the stockholders of the Company. Before making any voting or investment decision with respect to the acquisition, investors and stockholders of the Company are urged to read the proxy statement and the other relevant materials because they contain important information about the acquisition. The proxy statement and other relevant materials, and any other documents filed by the Company with the SEC, may be obtained free of charge from the Company by directing a request to the Company’s Investor Relations Department at toll free phone number 888-922-9711, email address InvestorRelations@odsyhealth.com or through the Company Web site www.odsyhealth.com under “Investor Relations — InfoRequest.”

Participants in the Solicitation

The Company and its directors and executive officers may be deemed to be participants in the solicitation of proxies from the Company’s stockholders in connection with the merger. Information about the Company’s directors and executive officers is set forth in the Company’s proxy statement on Schedule 14A filed with the SEC on April 5, 2010 and the Company’s Annual Report on Form 10-K filed on March 10, 2010. Additional information regarding the interests of participants in the solicitation of proxies in connection with the merger is included in the Company’s proxy statement.

-MORE-

ODSY Expects Second Quarter Diluted EPS Attributable

to Odyssey Stockholders of $0.39 to $0.41

Page 2

July 19, 2010

Forward-looking Statements

Certain statements contained in this press release are forward-looking statements within the meaning of the federal securities laws. Such forward-looking statements are based on management’s current expectations and are subject to known and unknown risks, uncertainties and assumptions which may cause the forward-looking events and circumstances discussed in this press release to differ materially from those anticipated or implied by the forward-looking statements. Additional risks, uncertainties and assumptions include, but are not limited to, general market conditions; adverse changes in reimbursement levels under Medicare and Medicaid programs; government and private party legal proceedings and investigations; adverse changes in the Medicare payment cap limits and increases in the Company’s estimated Medicare cap contractual adjustment; declines in patient census growth; increases in inflation including inflationary increases in patient care costs; the Company’s ability to effectively implement the Company’s 2010 operations and development strategies; the Company’s dependence on patient referral sources and potential adverse changes in patient referral practices of those referral sources; the Company’s ability to successfully integrate and operate acquired hospice programs; the ability to attract and retain healthcare professionals; increases in the Company’s bad debt expense due to various factors including an increase in the volume of pre-payment reviews by the Company’s Medicare fiscal intermediaries; adverse changes in the state and federal licensure and certification laws and regulations; adverse results of regulatory surveys; delays in licensure and/or certification; cost of complying with the terms and conditions of the Company’s corporate integrity agreement; adverse changes in the competitive environment in which the Company operates; changes in state or federal income, franchise or similar tax laws and regulations; adverse impact of natural disasters; changes in the Company’s estimate of additional stock-based compensation costs; and the disclosures contained under the headings “Government Regulation and Payment Structure” in “Item 1. Business” and “Item 1A. Risk Factors” of the Company’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 10, 2010, and in its other filings with the Securities and Exchange Commission. In addition to the risks, uncertainties and assumptions listed above, the Company faces risks associated with the Agreement and Plan of Merger, dated as of May 23, 2010, among the Company, Gentiva Health Services, Inc. and GTO Acquisition Corp. (attached as Exhibit 2.1 to the Company’s Current Report on Form 8-K as filed with the Securities and Exchange Commission on May 24, 2010). Such risks, uncertainties and assumptions include, but are not limited to, the ability to obtain regulatory approval for the transaction; the expected timing of the completion of the transaction; management plans regarding the transaction; the inability to complete the transaction due to the failure to satisfy the conditions required to complete the transaction; the risk that the businesses of the Company and Gentiva will not be integrated successfully, or will take longer than anticipated; the risk that expected cost savings from the transaction will not be achieved or unexpected costs will be incurred; any statements of the plan, strategies and objectives of management for future operations; the risk that disruptions from the transaction will harm relationships with employees, referral sources, patients and suppliers; and the outcome of litigation and regulatory proceedings to which we may be a party. Many of these factors are beyond the ability of the Company to control or predict. Given these uncertainties, readers are cautioned not to place undue reliance on such forward-looking statements, which reflect management’s views only as of the date hereof. The Company undertakes no obligation to revise or update any of the forward-looking statements or publicly announce any updates or revisions to any of the forward-looking statements contained in this press release and in the presentation to reflect any change in the Company’s expectations with regard thereto or any change in events, conditions, circumstances or assumptions underlying such statements.

-END-

ODYSSEY HEALTHCARE INC 8-K