To ensure that the chosen dose and dosing schedule of romidepsin is both safe and able to induce HIV-1 expression in latently infected CD4+ T cells, the study is planned in two parts with the following specific objectives: Part A 1. The primary objective is to evaluate the safety and tolerability of romidepsin at a reduced dosing of 5 mg/m2 in HIV- infected patients. Part B 2.The primary objective is to measure the effect of treatment with Vacc-4x + rhuGM-CSF and cyclic romidepsin treatment on the HIV-1 latent reservoir in HIV-infected patients virologically suppressed on cART. The main hypothesis is that therapeutic use of a potent HDACi will lead to short-term increases in HIV-1 transcription and long-term reductions in the HIV-1 reservoir size due to increased levels and responsiveness of HIV-1-specific cytotoxic T lymphocytes in Vacc-4x immunized subjects.