Antiretroviral therapy (ART) generally reduces plasma HIV to undetectable levels, although virus persists in latently infected CD4+ T cells. In some individuals, viremia remains detectable despite adherence to ART and the absence of drug resistance mutations. In this issue of the JCI, Halvas et al. describe HIV RNA sequences from plasma of 8 donors with persistent viremia. Residual viremia was dominated by identical HIV-1 RNA sequences that remained relatively constant over 4 years. Plasma virus matched replication-competent virus cultured from CD4+ T cells. Integration site analysis confirmed the presence of large clones of infected cells. These results indicate that nonsuppressible viremia can be due to expanded clones of infected CD4+ T cells carrying replication-competent virus. The individuals described here represent extreme examples of a phenomenon that is seen in all infected individuals and that is a major barrier to curing HIV infection, the in vivo proliferation of latently infected cells.