Participants must be on HAART with a suppressed viral load (< 50 copies/ml) for at least the previous 12 months. They will be randomly assigned to one of two groups, one group will start the valproic acid right away at week 1 for 16 weeks, and the other group will wait until week 17 to add valproic acid to their treatment for 32 weeks. Subjects will be followed every four weeks for one year and evaluated by a variety of assays, all carried out using well-established methods, to assess the main outcome defined by changes in HIV reservoir size measured by the mean frequency of resting CD4 memory cells carrying HIV proviral DNA.