An extranuclear replication system, consisting of an orthogonal DNA plasmid-DNA polymerase pair, was developed in Saccharomyces cerevisiae. Engineered error-prone DNA polymerases showed complete mutational targeting in vivo: per-base mutation rates on the plasmid were increased substantially and remained stable with no increase in genomic rates. Orthogonal replication serves as a platform for in vivo continuous evolution and as a system whose replicative properties can be manipulated independently of the host's.