Replication-competent human immunodeficiency virus (HIV) persists in infected people despite suppressive combination antiretroviral therapy (cART), and it represents a major obstacle to HIV functional cure or eradication. We have developed a model of cART-mediated viral suppression in simian human immunodeficiency virus (SIV) mac239-infected Indian rhesus macaques and evaluated the impact of the histone deacetylase inhibitor (HDACi) romidepsin (RMD) on viremia in vivo. Eight macaques virologically suppressed to clinically relevant levels (<30 viral RNA copies/ml of plasma), using a three-class five-drug cART regimen, received multiple intravenous infusions of either RMD (n = 5) or saline (n = 3) starting 31 to 54 weeks after cART initiation. In vivo RMD treatment resulted in significant transient increases in acetylated histone levels in CD4⁺ T cells. RMD-treated animals demonstrated plasma viral load measurements for each 2-week treatment cycle that were significantly higher than those in saline control-treated animals during periods of treatment, suggestive of RMD-induced viral reactivation. However, plasma virus rebound was indistinguishable between RMD-treated and control-treated animals for a subset of animals released from cART. These findings suggest that HDACi drugs, such as RMD, can reactivate residual virus in the presence of suppressive antiviral therapy and may be a valuable component of a comprehensive HIV functional cure/eradication strategy.