The major obstacle to curing HIV infection is the persistence of cells with intact proviruses that can produce replication-competent virus. This HIV reservoir is believed to exist primarily in CD4+ T-cells and is stable despite years of suppressive antiretroviral therapy. A potential mechanism for HIV persistence is clonal expansion of infected cells, but how often such clones carry replication-competent proviruses has been controversial. Here, we used single-genome sequencing to probe for identical HIV sequence matches among viruses recovered in different viral outgrowth cultures and between the sequences of outgrowth viruses and proviral or intracellular HIV RNA sequences in uncultured blood mononuclear cells from eight donors on suppressive ART with diverse proviral populations. All eight donors had viral outgrowth virus that was fully susceptible to their current ART drug regimen. Six of eight donors studied had identical near full-length HIV RNA sequences recovered from different viral outgrowth cultures, and one of the two remaining donors had identical partial viral sequence matches between outgrowth virus and intracellular HIV RNA. These findings provide evidence that clonal expansion of HIV-infected cells is an important mechanism of reservoir persistence that should be targeted to cure HIV infection.