Enteroviruses are causative agents of a range of human diseases. The replication of these viruses within cells relies on specialized membranous structures termed replication organelles (ROs) that form during infection but whose origin remains elusive. To capture the emergence of enterovirus ROs, we use correlative light and serial block-face scanning electron microscopy, a powerful method to pinpoint rare events in their whole-cell ultrastructural context. RO biogenesis was found to occur first at ER and then at Golgi membranes. Extensive contacts were found between early ROs and lipid droplets (LDs), which likely serve to provide LD-derived lipids required for replication. Together, these data establish the dual origin of enterovirus ROs and the chronology of their biogenesis at different supporting cellular membranes.