The Rudiviridae are a family of rod-shaped archaeal viruses with covalently closed, linear double-stranded DNA (dsDNA) genomes. Their replication mechanisms remain obscure, although parallels have been drawn to the Poxviridae and other large cytoplasmic eukaryotic viruses. Here we report that a protein encoded in the 34-kbp genome of the rudivirus SIRV1 is a member of the replication initiator (Rep) superfamily of proteins, which initiate rolling-circle replication (RCR) of diverse viruses and plasmids. We show that SIRV Rep nicks the viral hairpin terminus, forming a covalent adduct between an active-site tyrosine and the 5' end of the DNA, releasing a 3' DNA end as a primer for DNA synthesis. The enzyme can also catalyze the joining reaction that is necessary to reseal the DNA hairpin and terminate replication. The dimeric structure points to a simple mechanism through which two closely positioned active sites, each with a single tyrosine residue, work in tandem to catalyze DNA nicking and joining. We propose a novel mechanism for rudivirus DNA replication, incorporating the first known example of a Rep protein that is not linked to RCR. The implications for Rep protein function and viral replication are discussed.