Residual viremia is common during antiretroviral therapy (ART) and could be caused by ongoing low-level virus replication or by release of viral particles from infected cells. ART intensification should impact ongoing viral propagation but not virion release. Eighteen acutely infected men were enrolled in a randomized controlled trial and monitored for a median of 107 weeks. Participants started ART with ( n = 9) or without ( n = 9) intensification with maraviroc (MVC) within 90 days of infection. Levels of HIV DNA and cell-free RNA were quantified by droplet digital PCR. Deep sequencing of C2-V3 env , gag , and pol (454 Roche) was performed on longitudinally collected plasma and peripheral blood mononuclear cell (PBMC) samples while on ART. Sequence data were analyzed for evidence of evolution by (i) molecular diversity analysis, (ii) nonparametric test for panmixia, and (iii) tip date randomization within a Bayesian framework. There was a longitudinal decay of HIV DNA after initiation of ART with no difference between MVC intensification groups (–0.08 ± 0.01 versus –0.09 ± 0.01 log 10 copies/week in MVC + versus MVC – groups; P = 0.62). All participants had low-level residual viremia (median, 2.8 RNA copies/ml). Across participants, medians of 56 (interquartile range [IQR], 36 to 74), 29 (IQR, 25 to 35), and 40 (IQR, 31 to 54) haplotypes were generated for env , gag , and pol regions, respectively. There was no clear evidence of viral evolution during ART and no difference in viral diversity or population structure from individuals with or without MVC intensification. Further efforts focusing on elucidating the mechanism(s) of viral persistence in various compartments using recent sequencing technologies are still needed, and potential low-level viral replication should always be considered in cure strategies. IMPORTANCE Residual viremia is common among HIV-infected people on ART. It remains controversial if this viremia is a consequence of propagating infection. We hypothesized that molecular evolution would be detectable during viral propagation and that therapy intensified with the entry inhibitor maraviroc would demonstrate less evolution. We performed a randomized double-blinded treatment trial with 18 acutely infected men (standard ART versus standard ART plus maraviroc). From longitudinally collected blood plasma and cells, levels of HIV DNA and cell-free HIV RNA were quantified by droplet digital PCR, and HIV DNA ( env , gag , and pol coding regions) was deep sequenced (454 Roche). Investigating people who started ART during the earliest stages of their HIV infection, when viral diversity is low, provides an opportunity to detect evidence of viral evolution. Despite using a battery of analytical techniques, no clear and consistent evidence of viral propagation for over 90 weeks of observation could be discerned.