Genasense, Carboplatin, Paclitaxel (GCP) Combination in Uveal Melanoma

Study Drugs: Oblimersen is designed to stop the body from making a protein that makes melanoma cells resistant to chemotherapy drugs. This may make carboplatin and/or paclitaxel more effective. Carboplatin is designed to interfere with the growth of cancer cells by stopping cell division, which may cause the cells to die. Paclitaxel is designed to block cancer cells from dividing, which may cause them to die. Study Drug Administration: If you are found to be eligible to take part in this study, you will receive oblimersen by vein over about 1 hour (+/- 5 minutes) on Days 1, 3, and 5 of each 21-day study "cycle." You will receive dexamethasone by vein over about 30 minutes before you receive oblimersen to help prevent side effects. You will take ibuprofen by mouth about 30 minutes before you receive oblimersen. You will receive paclitaxel by vein over about 3 hours (+/- 5 minutes) on Day 3 of each cycle. You will receive carboplatin by vein over about 30 minutes (+/- 5 minutes) on Day 3 of each cycle. Before you receive each of these drugs, you may receive other drugs to help prevent side effects (such as nausea, vomiting, fever, and/or body aches). You may need to receive some of these drugs for some time after you receive the study drugs. Your doctor will tell you more about each of these drugs, about how they are given, and about any possible risks of receiving them. Study Visits: Within 3 days before each cycle, blood (about 1 tablespoon) will be drawn for routine tests. On Day 1 of each cycle: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * You will be asked about any side effects you may be having. * Women who are able to become pregnant will have a routine urine pregnancy test done. Each week while you are on study, blood (about 1 teaspoon) will be drawn for routine tests. Every 6 weeks, you will have the same imaging (CT and/or MRI) scans that you had at screening to check the status of the disease. If the doctor thinks it is needed, you will have a bone scan. Length of Study: You may continue taking the study drugs for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drugs if the disease gets worse or intolerable side effects occur. Your participation on the study will be over once you have completed the end-of-treatment visit and follow-up. End-of-Treatment Visit: After you stop receiving the study drugs, the following tests and procedures will be performed: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. * You will be asked about any side effects you may have had. * You will have the same imaging (CTand /or MRI) scans that you had at screening to check the status of the disease. * Women who are able to become pregnant will have a routine urine pregnancy test done. Follow-up: Every 3 months for up to 2 years after you stop receiving the study drugs, you will be called and asked about how you are doing and about any other drugs you may be receiving. Each call will last about 3 minutes. This is an investigational study. Carboplatin and paclitaxel are FDA approved and commercially available for the treatment of a variety of cancers including breast, lung, and ovarian cancers. Oblimersen is not FDA approved or commercially available. It is currently being used for research purposes only. Up to 30 patients will take part in this study. All will be enrolled at MD Anderson.