The goal of this clinical research study is to learn if ipilimumab in combination with either Lupron® (leuprolide), Zoladex® (goserelin), or Firmagon® (degarelix) can affect prostate-specific antigen (PSA) levels in patients with prostate cancer. Researchers also want to learn if these drug combinations affect the body's immune system. The safety of these drug combinations will also be studied.

The Study Drugs: Ipilimumab is designed to block the activity of cells that decrease the immune system's ability to fight cancer. Leuprolide, goserelin, and degarelix are designed to help stop the body from making testosterone (a male sex hormone that prostate cancer cells need to survive), which may slow the growth of cancer cells. Study Drug Administration: If you are found to be eligible to take part in this study, you will receive either leuprolide, goserelin or degarelix . The drug you receive will depend on what the doctor thinks is in your best interest and/or which drug your insurance provider will help to cover. Leuprolide is given through a needle in the muscle. Goserelin and degarelix are given through a needle under the skin in the abdomen. Beginning at Week 1, you will receive the drug 1 time every month or every 3 months for up to 8 months. Your doctor will tell you more about which dosing schedule you will use. You will also receive ipilimumab by vein over about 90 minutes at Weeks 5, 9, 13, and 17. Your blood pressure will be measured every 30 minutes during the infusion, as well as an hour after you are finished receiving the drug. Study Visits: Before each dose of ipilimumab, and every 4 weeks for 6 months after the last dose of ipilimumab, and every 12 weeks after that, the following tests and procedures will be performed: * You will have a physical exam. * You will be asked about any other drugs and/or treatments you may be receiving. * You will be asked about any side effects you may have experienced. * Your performance status will be recorded. * Blood (about 3 teaspoons) will be drawn for routine tests and to measure your protein, PSA, and testosterone levels, and to check the function of your pancreas, thyroid, and adrenal glands. * Urine will be collected for routine tests. * This blood will also be tested for other hormone levels to check the function of your thyroid and adrenal glands (before each dose of ipilimumab and 4 weeks after the last dose only). Every 12 weeks, you will have the same imaging scans that you had at screening. Length of Study: You may receive the study drugs for up to 8 months. You will remain on study for as long as the disease remains stable. You will be taken off study treatment if you have intolerable side effects or if the disease gets worse. End-of-Study Treatment/Observation Visit: Within 14 days after your disease gets worse, the following tests and procedures will be performed: * You will have a physical exam. * You will be asked about any drugs and/or treatments you may be receiving. * You will be asked about any side effects you may have experienced. * Blood (about 3 teaspoons) will be drawn for routine tests. This blood will also be tested to measure your protein, PSA, and testosterone levels, and to check the function of your pancreas, thyroid, and adrenal glands. * You will have the same imaging scans that you had at screening. Long-Term Follow-Up: A member of the study staff will check up on you about every 6 months after your End-of-Study Treatment/Observation Visit. This will consist of a phone call, an e-mail, or a review of your medical and/or other records. If you are contacted by phone, the call will only last a few minutes. This is an investigational study. Leuprolide, goserelin, and degarelix are FDA approved and commercially available for the treatment of prostate cancer. Ipilimumab is FDA approved and commercially available for melanoma. Its use to treat prostate cancer is investigational. Up to 48 patients will take part in this study. All will be enrolled at MD Anderson.