Kaposi's sarcoma-associated herpesvirus (KSHV) latently infects tumor cells and persists as a multiple-copy, extrachromosomal, circular episome. To persist, the viral genome must replicate with each cell cycle. The KSHV latency-associated nuclear antigen (LANA) mediates viral DNA replication and persistence, but little is known regarding the underlying mechanisms. We find that LANA recruits replication factor C (RFC), the DNA polymerase clamp [proliferating cell nuclear antigen (PCNA)] loader, to drive DNA replication efficiently. Mutated LANA lacking RFC interaction was deficient for LANA-mediated DNA replication and episome persistence. RFC depletion had a negative impact on LANA’s ability to replicate and maintain viral DNA in cells containing artificial KSHV episomes or in infected cells, leading to loss of virus. LANA substantially increased PCNA loading onto DNA in vitro and recruited RFC and PCNA to KSHV DNA in cells. These findings suggest that PCNA loading is a rate-limiting step in DNA replication that is incompatible with viral survival. LANA enhancement of PCNA loading permits efficient virus replication and persistence, revealing a previously unidentified mechanism for KSHV latency.