The persistence of the HIV reservoir in infected individuals is a major obstacle to the development of a cure for HIV. Here, using an in vitro model of HIV-infected quiescent CD4 T cells, we reveal a gene expression signature of 103 upregulated genes that are specific for latently infected cells, including genes for 16 transmembrane proteins. In vitro screening for surface expression in HIV-infected quiescent CD4 T cells shows that the low-affinity receptor for the immunoglobulin G Fc fragment, CD32a, is the most highly induced, with no detectable expression in bystander cells. Notably, productive HIV-1 infection of T-cell-receptor-stimulated CD4 T cells is not associated with CD32a expression, suggesting that a quiescence-dependent mechanism is required for its induction. Using blood samples from HIV-1-positive participants receiving suppressive antiretroviral therapy, we identify a subpopulation of 0.012% of CD4 T cells that express CD32a and host up to three copies of HIV DNA per cell. This CD32a+ reservoir was highly enriched in inducible replication-competent proviruses and can be predominant in some participants. Our discovery that CD32a+ lymphocytes represent the elusive HIV-1 reservoir may lead to insights that will facilitate the specific targeting and elimination of this reservoir.