Kaposi's Sarcoma-associated herpesvirus (KSHV) is maintained as a stable episome in latently infected pleural effusion lymphoma (PEL) cells. Episome maintenance is conferred by the binding of the KSHV-encoded LANA protein to the viral terminal repeats (TR). Here, we show that DNA replication in the KSHV TR is coupled with DNA recombination and mediated in part through the cellular replication fork protection factors Timeless (Tim) and Tipin. We show by two-dimensional (2D) agarose gel electrophoresis that replication forks naturally stall and form recombination-like structures at the TR during an unperturbed cell cycle. Chromatin immunoprecipitation (ChIP) assays revealed that Tim and Tipin are selectively enriched at the KSHV TR during S phase and in a LANA-dependent manner. Tim depletion inhibited LANA-dependent TR DNA replication and caused the loss of KSHV episomes from latently infected PEL cells. Tim depletion resulted in the aberrant accumulation of recombination structures and arrested MCM helicase at TR. Tim depletion did not induce the KSHV lytic cycle or apoptotic cell death. We propose that KSHV episome maintenance requires Tim-assisted replication fork protection at the viral terminal repeats and that Tim-dependent recombination-like structures form at TR to promote DNA repeat stability and viral genome maintenance.