The origin of the eukaryotic cell cycle, including mitosis, meiosis, and sex are as yet unresolved aspects of the evolution of the eukaryotes. The wide phylogenetic distribution of both mitosis and meiosis suggest that these processes are integrally related to the origin of the earliest eukaryotic cells. According to the viral eukaryogenesis (VE) hypothesis, the eukaryotes are a composite of three phylogenetically unrelated organisms: a viral lysogen that evolved into the nucleus, an archaeal cell that evolved into the eukaryotic cytoplasm, and an alpha-proteobacterium that evolved into the mitochondria. In the extended VE hypothesis presented here, the eukaryotic cell cycle arises as a consequence of the derivation of the nucleus from a lysogenic DNA virus.