The capacity of HIV-1 to replicate during optimal antiretroviral therapy (ART) is challenging to assess directly. To gain greater sensitivity to detect evolution on ART, we used a nonhuman primate (NHP) model providing precise control over the level of pre-ART evolution and more comprehensive analyses than are possible with clinical samples. We infected 21 rhesus macaques (RMs) with the barcoded virus SIVmac239M and initiated ART early to minimize baseline genetic diversity. RMs were treated for 285-1200 days. We used several tests of molecular evolution to compare 1352 near-full-length (nFL) SIV DNA single genome sequences from PBMCs, lymph nodes, and spleen obtained near the time of ART initiation and those present after long-term ART, none of which showed significant changes to the SIV DNA population during ART in any animal. To investigate the possibility of ongoing replication in unsampled putative tissue sanctuaries during ART, we discontinued treatment in four animals and confirmed that none of the 336 nFL SIV RNA sequences obtained from rebound plasma viremia showed evidence of evolution. The rigorous nature of our analyses reinforced the emerging consensus of a lack of appreciable ongoing replication on effective ART and validates the relevance of this NHP model for cure studies.