Background: Whether ongoing virus replication occurs in HIV-infected individuals on antiretroviral therapy (ART) is unclear; therefore, whether residual virus replication is a barrier to achieving a cure for HIV is also unknown. We aimed to establish whether ART intensification with dolutegravir would reveal or affect residual virus replication in HIV-infected individuals on suppressive treatment. Methods: In this randomised, placebo-controlled, double-blind trial, we enrolled HIV-infected adults (aged 18 years and older) receiving combination ART (at least three agents) for at least 3 years from the Alfred Hospital and Melbourne Sexual Health Centre, Melbourne, VIC, Australia. Eligible participants had fewer than 50 copies per mL HIV-1 plasma RNA for more than 3 years and fewer than 20 copies per mL at screening and two CD4 counts higher than 350 cells per μL in the previous 24 months including screening. Participants were randomly assigned (1:1) to receive 50 mg oral dolutegravir or placebo once a day for 56 days in addition to background ART. Follow-up was done at days 1, 3, 7, 14, 28, 56, and 84. The primary outcome was the change from baseline in frequency of 2-long terminal repeat (2-LTR) circles in peripheral blood CD4 cells at day 7. This trial is registered with ClinicalTrials.gov, number NCT02500446. Findings: Between Sept 21, 2015, and Sept 19, 2016, 46 individuals were screened for inclusion. 40 were eligible for inclusion and were randomly assigned to the dolutegravir (n=21) or placebo group (n=19). All enrolled participants completed the study procedures and no individuals were lost to follow up. All participants were on suppressive ART with 12% receiving protease inhibitors and the others non-nucleoside reverse transcriptase inhibitors. Median 2-LTR circles fold-change from baseline to day 7 was −0·17 (IQR −0·90 to 0·90) in the dolutegravir group and −0·26 (−1·00 to 1·17) in the placebo group (p=0·17). The addition of dolutegravir to pre-existing ART regimens was safe and there were no treatment discontinuations or treatment-related serious adverse events. Interpretation: Our findings show that in HIV-infected individuals on modern suppressive ART regimens, residual replication is rare, if at all present, and was not recorded in blood after dolutegravir intensification. Because tissue biopsies were not done we cannot exclude the possibility of residual virus replication in tissue. Strategies other than ART alone are needed to eliminate HIV persistence on treatment. Funding: ViiV Healthcare.