The spontaneous transition of Epstein-Barr virus (EBV) from latency to productive infection is infrequent, making its analysis in the resulting mixed cell populations difficult. We engineered cells to support this transition efficiently and developed EBV DNA variants that could be visualized and measured as fluorescent signals over multiple cell cycles. This approach revealed that EBV's productive replication began synchronously for viral DNAs within a cell but asynchronously between cells. EBV DNA amplification was delayed until early S phase and occurred in factories characterized by the absence of cellular DNA and histones, by a sequential redistribution of PCNA, and by localization away from the nuclear periphery. The earliest amplified DNAs lacked histones accompanying a decline in four histone chaperones. Thus, EBV transits from being dependent on the cellular replication machinery during latency to commandeering both that machinery and nuclear structure for its own reproductive needs.