Participants in this study will be randomly assigned to receive either the therapeutic vaccine or placebo in addition to their regular HAART regimens. During the first part of the study, participants will receive 4 vaccinations at Weeks 0, 4, 8 and 24. All individuals completing the therapeutic vaccination phase (defined as completing at least 3 immunizations, including the Week 24 immunization) will be given the opportunity to participate in the second part of the study and undergo a supervised discontinuation of HAART. At Week 30, these participants will discontinue all antiretroviral treatment and will be closely monitored. Participants will restart HAART if they experience a significant decline in their CD4 count, an increase in their viral loads, or if their physicians recommend they resume HAART. At Week 52, all other participants can restart HAART at the discretion of their primary physician.