HIV-1-specific CD8+ T cells are an important component of HIV-1 curative strategies. Viral variants in the HIV-1 reservoir may limit the capacity of T cells to detect and clear virus-infected cells. We investigated the patterns of T cell escape variants in the replication-competent reservoir of 25 persons living with HIV-1 (PLWH) durably suppressed on antiretroviral therapy (ART). We identified all reactive T cell epitopes in the HIV-1 proteome for each participant and sequenced HIV-1 outgrowth viruses from resting CD4+ T cells. All non-synonymous mutations in reactive T cell epitopes were tested for their effect on the size of the T cell response, with a≥50% loss defined as an escape mutation. The majority (68%) of T cell epitopes harbored no detectable escape mutations. These findings suggest that circulating T cells in PLWH on ART could contribute to control of rebound and could be targeted for boosting in curative strategies.