A number of molecular forms of DNA polymerases have been reported to be involved in eukaryotic nuclear DNA replication, with contributions from alpha-, delta-, and epsilon-polymerases. It has been reported that delta-polymerase possessed a central role in DNA replication in archaea, whose ancestry are thought to be closely related to the ancestor of eukaryotes. Indeed, in vitro experiment shown here suggests that delta-polymerase has the potential ability to start DNA synthesis immediately after RNA primer synthesis. Therefore, the question arises, where did the alpha-polymerase come from? Phylogenetic analysis based on the nucleotide sequence of several conserved regions reveals that two poxviruses, vaccinia and variola viruses, have polymerases similar to eukaryotic alpha-polymerase rather than delta-polymerase, while adenovirus, herpes family viruses, and archaeotes have eukaryotic delta-like polymerases, suggesting that the eukaryotic alpha-polymerase gene is derived from a poxvirus-like organism, which had some eukaryote-like characteristics. Furthermore, the poxvirus's proliferation independent from the host-cell nucleus suggests the possibility that this virus could infect non-nucleated cells, such as ancestral eukaryotes. I wish to propose here a new hypothesis for the origin of the eukaryotic nucleus, posing symbiotic contact of an orthopoxvirus ancestor with an archaebacterium, whose genome already had a delta-like polymerase gene.