Human T-lymphotropic virus type-1 (HTLV-1) persists within hosts via infectious spread (de novo infection) and mitotic spread (infected cell proliferation), creating a population structure of multiple clones (infected cell populations with identical genomic proviral integration sites). The relative contributions of infectious and mitotic spread to HTLV-1 persistence are unknown, and will determine the efficacy of different approaches to treatment. The prevailing view is that infectious spread is negligible in HTLV-1 persistence beyond early infection. However, in light of recent high-throughput data on the abundance of HTLV-1 clones, and recent estimates of HTLV-1 clonal diversity that are substantially higher than previously thought (typically between 10⁴ and 10⁵ HTLV-1⁺ T cell clones in the body of an asymptomatic carrier or patient with HTLV-1-associated myelopathy/tropical spastic paraparesis), ongoing infectious spread during chronic infection remains possible. We estimate the ratio of infectious to mitotic spread using a hybrid model of deterministic and stochastic processes, fitted to previously published HTLV-1 clonal diversity estimates. We investigate the robustness of our estimates using three alternative estimators. We find that, contrary to previous belief, infectious spread persists during chronic infection, even after HTLV-1 proviral load has reached its set point, and we estimate that between 100 and 200 new HTLV-1 clones are created and killed every day. We find broad agreement between all estimators. The risk of HTLV-1-associated malignancy and inflammatory disease is strongly correlated with proviral load, which in turn is correlated with the number of HTLV-1-infected clones, which are created by de novo infection. Our results therefore imply that suppression of de novo infection may reduce the risk of malignant transformation.