Adjuvant Therapy of Pegylated Interferon- 2b Plus Melanoma Peptide Vaccine

The Study Drugs: Pegylated Interferon alfa-2b is a protein made by the human immune system that helps to fight viral infections and regulate cell function. Gp100 is a protein that is found on melanoma cells. In laboratory studies, the gp100 vaccine has been shown to stimulate the immune system to "recognize" and kill melanoma cells that have gp100 on their cell surfaces. Evaluation of Immune cell response to vaccine: Blood (about 3-1/2 tablespoons) will be drawn on Weeks 4, 7,10,13,16,19, and 22 for tests to check the response of your immune system to the vaccine, before each injection. These tests are for research purposes only and will not be used to make decisions about your medical care. Parts of the Study: There are 2 parts to this study, an Induction Phase and a Maintenance Phase. The Induction Phase treatment is the first course of treatment used to stimulate ("turn on") an immune-cell response to fight cancer and to learn the body's response to the treatment. The Maintenance Phase treatment is continued therapy and is used to maintain the immune-cell response and to help keep the disease in remission. Study Groups: If participant is found to be eligible to take part in this study, they will be randomly assigned (as in the roll of dice) to 1 of 3 treatment groups. Participant will have an equal chance of being assigned to one of each of the groups. Participants in each group will receive the same dose levels of pegylated Interferon alfa-2b and gp100. The difference between each group will be the dosing schedule of pegylated Interferon alfa-2b. Every week, participant will give themselves the pegylated Interferon alfa-2b either in the clinic or at home, and the gp100 will be given to participant every 3 weeks by the research nurse in the clinic. Participant will be shown how to give yourself Pegylated Interferon alfa-2b at home. Pegylated Interferon alfa-2b will be given immediately after the GP-100 Peptide Vaccine injection. Participants in Group 1 will take pegylated Interferon alfa-2b at a certain dose level once a week for 4 weeks (in the Induction Phase), followed by once a week for 20 weeks in the Maintenance Phase (when the drug will be taken at a lower dose level than during Induction). Participants in Group 2 will take pegylated Interferon alfa-2b at a certain dose level once a week for 8 weeks (in the Induction Phase), followed by once a week for 16 weeks in the Maintenance Phase (when the drug will be taken at a lower dose level than during Induction). Participants in Group 3 will take pegylated Interferon alfa-2b at a certain dose level once a week for 12 weeks (in the Induction Phase), followed by once a week for 12 weeks in the Maintenance Phase (when the drug will be taken at a lower dose level than during Induction). Study Treatment: Participant will take pegylated Interferon alfa-2b as an injection just under their skin. Participant will receive gp100 as an injection just under their skin once every 3 weeks. On Week 1, PEG-Intron will be given right after GP-100 Peptide Vaccine injection in the clinic. Participant will be observed for at least 30 minutes after both GP-100 Peptide Vaccine and PEG-Intron Injections. On Weeks 4, 7, 10, 13, 16, 19, and 22 (+/- 1 day, not counting institutional holidays), GP-100 peptide will be given in the clinic. Participant will be observed for at least 30 minutes after GP-100 Peptide Vaccine injection. Participant should give the PEG-Intron to themselves within 24 hours of GP-100 Peptide Vaccine injection. The injection of gp100 will be given in two separate areas of participant's limbs, such as in an upper arm or thigh. It will be given in the same area each time. Length of Study: Participant will remain on this study for up to 25 weeks, unless the disease comes out of remission or they experience intolerable side effects. End-of-Treatment Visit: At the end of study treatment (approximately 3 weeks after the last injection of gp100), participant will have the following tests: * Participant will have a review of their general health and any medical problems they may be having. * Participant will have a physical exam, including measurement of their vital signs. * Blood (about 1 tablespoon) will be drawn for routine tests. * Participant will have the leukapheresis repeated. * Participant will have a CT scan of chest, stomach, and pelvis, and they will have an MRI or CT scan of the brain. While participant is on this study no steroids will be allowed while on treatment. This is an investigational study. Pegylated Interferon alfa-2b is FDA approved and commercially available for the treatment of chronic hepatitis C. Gp100 is not FDA approved or commercially available. At this time, the combination use of pegylated Interferon alfa-2b plus gp100 is being used for research purposes only in this study. Up to 30 participants will take part in this study. All will be enrolled at MD Anderson.