1. CD4+ T-cell count <350 cells/µL or detectable plasma HIV RNA (>50 copies HIV RNA/mL) within the past 12-months. During the study, if CD4+ T-cell count declines by >100 cells/µL, or if plasma HIV RNA becomes detectable (>50 copies HIV RNA/mL after repeat analysis 2wks apart), and the participant denies any lapse in their anti-HIV medication regimen, the study medication will be stopped and an adverse event documented. If at any time during the study, two participants experience a reduction in T-cell count >100 cells/µL, or their plasma HIV RNA levels become detectable (>50 copies HIV RNA/mL after repeat analysis 2wks apart), and they are confirmed (by unblinding) to have received sitagliptin, the study will be stopped for serious safety concerns.