A primary objective of this study is to assess the safety and toxicity of mDAPTA (Adaptavir) in HIV infected individuals with suppressed viral loads with HAART treatment and assess the proportion of study participants achieving PMBC viral culture negative status at 24weeks. PMBC viral culture status is a direct measurement of treatment resistant, residual, active HIV replication in the peripheral blood mononuclear cells. We hypothesize this proportion will be significantly greater in the treatment arm relative to the placebo arm (the odds of achieving this endpoint are significantly greater in mDAPTA- than in placebo-treated participants).