Therapeutic Vaccine for HIV

Background: \- In most people who have human immunodeficiency virus (HIV), the immune system cannot control or cure the infection. Antiretroviral therapy drugs can keep the amount of HIV virus low for a long time. However, this treatment does not remove the virus from the body. In the vast majority of patients antiretroviral therapy also will not protect the body from the virus once treatment stops. Researchers want to see if therapeutic vaccination can help people with HIV. Therapeutic vaccination means giving vaccines to treat an infection that someone already has (HIV, in this case). It may help the body's immune system attack the infection. This study will look at different measures of HIV infection after receiving either therapeutic vaccination or a placebo. Objectives: \- To see whether therapeutic vaccination is safe and can affect how the body responds to HIV infection. Eligibility: \- Individuals between 18 and 65 years of age who have HIV and are taking antiretroviral therapy drugs. Design: * Participants will be screened with a physical exam and medical history. Blood and urine samples will be collected. * During the screening visit and throughout the study until week 56, participants will continue to take their HIV medications. * Participants will be divided into two groups. One group will have the study vaccines. The other will have a placebo. * The first study vaccine or placebo will be given in weeks 4, 12, and 36. The second study vaccine or the placebo will be given in weeks 24 and 48. Blood samples and other tests will be given at each visit. * After the study visit at week 56, participants will stop their HIV medications until week 72. From weeks 58 through 72, they will come in every 2 weeks for study visits; each visit will take about 1 hour to complete. These visits will look at the body s response to the vaccines and their HIV viral load. After week 72, participants will re-start their HIV medications. * There will be follow-up study vi