Although antiretroviral therapy (ART) is highly effective at suppressing HIV-1 replication, the virus persists as a latent reservoir in resting CD4+ T cells during therapy. This reservoir forms even when ART is initiated early after infection, but the dynamics of its formation are largely unknown. The viral reservoirs of individuals who initiate ART during chronic infection are generally larger and genetically more diverse than those of individuals who initiate therapy during acute infection, consistent with the hypothesis that the reservoir is formed continuously throughout untreated infection. To determine when viruses enter the latent reservoir, we compared sequences of replication-competent viruses from resting peripheral CD4+ T cells from nine HIV-positive women on therapy to viral sequences circulating in blood collected longitudinally before therapy. We found that, on average, 71% of the unique viruses induced from the post-therapy latent reservoir were most genetically similar to viruses replicating just before ART initiation. This proportion is far greater than would be expected if the reservoir formed continuously and was always long lived. We conclude that ART alters the host environment in a way that allows the formation or stabilization of most of the long-lived latent HIV-1 reservoir, which points to new strategies targeted at limiting the formation of the reservoir around the time of therapy initiation.