This is a phase I/II, open label, single-arm, single-site clinical trial designed to evaluate the safety and antiviral activity of the ApB DC vaccine, a therapeutic vaccine derived from autologous dendritic cells loaded with autologous HIV-1 infected apoptotic cells. The study will be conducted in three phases. The first is the pre-vaccination phase that includes study entry, isolation of autologous virus, and initiation of antiretroviral therapy. Once the patient's viral load has been suppressed to undetectable levels (<50 copies/mL) and sufficient virus has been isolated, the second phase will begin. This includes leukapheresis in order to harvest monocytes and lymphocytes necessary for vaccine preparation. Three vaccine doses will be administered subcutaneously every other week. Six weeks after the last vaccination, the third phase, analytic treatment interruption (ATI) phase, will begin. A fourth, booster dose of vaccine will be given two weeks after the start of treatment interruption. The treatment interruption will be continued for twelve weeks after which the primary HIV provider will decide whether or not antiretroviral therapy should be restarted. CD4 and viral load will be closely monitored throughout the study especially during treatment interruption. Follow-up will be continued for 24 weeks after the 12-week treatment interruption.