Antiretroviral therapy (ART) suppresses viral replication in people living with HIV. Yet, infected cells persist for decades on ART and viremia returns if ART is stopped. Persistence has been attributed to viral replication in an ART sanctuary and long-lived and/or proliferating latently infected cells. Using ecological methods and existing data, we infer that >99% of infected cells are members of clonal populations after one year of ART. We reconcile our results with observations from the first months of ART, demonstrating mathematically how a fossil record of historic HIV replication permits observed viral evolution even while most new infected cells arise from proliferation. Together, our results imply cellular proliferation generates a majority of infected cells during ART. Therefore, reducing proliferation could decrease the size of the HIV reservoir and help achieve a functional cure.