The eukaryotic replicative DNA polymerases are similar to those of large DNA viruses of eukaryotic and bacterial T4 phages but not to those of eubacteria. We develop and examine the hypothesis that DNA virus replication proteins gave rise to those of eukaryotes during evolution. We chose the DNA polymerase from phycodnavirus (which infects microalgae) as the basis of this analysis, as it represents a virus of a primitive eukaryote. We show that it has significant similarity with replicative DNA polymerases of eukaryotes and certain of their large DNA viruses. Sequence alignment confirms this similarity and establishes the presence of highly conserved domains in the polymerase amino terminus. Subsequent reconstruction of a phylogenetic tree indicates that these algal viral DNA polymerases are near the root of the clade containing all eukaryotic DNA polymerase delta members but that this clade does not contain the polymerases of other DNA viruses. We consider arguments for the polarity of this relationship and present the hypothesis that the replication genes of DNA viruses gave rise to those of eukaryotes and not the reverse direction.