Thus, there are several unresolved issues related to residual viral replication in the presence of ART and the potential benefit of integrase inhibitors in this context: How frequent is this phenomenon and does it occur more frequently in patients receiving a PI-containing regimen? Given that raltegravir does seem to impact residual replication in approximate 30% of HIV infected patients on ART when assessed early after intensification, what is the effect of DTG in this setting? Finally, what are the dynamics of 2-LTR levels in blood in the early phases after intensification with an integrase inhibitor? To address those questions, the investigators have designed a randomized, controlled study to compare the impact of intensification with DTG or placebo in HIV-infected patients on suppressive ART. In this study, the investigators will closely define the effects of dolutegravir intensification on 2-LTR levels in circulating CD4+ T cells.