The capacity of HIV-1 to establish latent infection of CD4⁺ T cells may allow viral persistence despite immune responses and antiretroviral therapy. Measurements of infectious virus^1,2 and viral RNA^3,4 in plasma and of infectious virus¹, viral DNA^5–10 and viral messenger RNA species^11–14 in infected cells all suggest that HIV-1 replication continues throughout the course of infection. Uncertainty remains over what fraction of CD4⁺ T cells are infected and whether there are latent reservoirs for the virus. We show here that during the asymptomatic phase of infection there is an extremely low total body load of latently infected resting CD4⁺ T cells with replication-competent integrated pro virus (<10⁷ cells). The most prevalent form of HIV-1 DNA in resting and activated CD4⁺ T cells is a full-length, linear, unintegrated form that is not replication competent. The infection progresses even though at any given time in the lymphoid tissues integrated HIV-1 DNA is present in only a minute fraction of the susceptible populations, including resting and activated CD4⁺ T cells and macrophages.