The Trf4p/Pol sigma DNA polymerase (formerly Trf4p/Pol kappa) couples DNA replication to the establishment of sister chromatid cohesion. The polymerase is encoded by two redundant homologs in Saccharomyces cerevisiae, TRF4 and TRF5, that together define a fourth essential nuclear DNA polymerase in yeast and probably in all eukaryotes. Here we present a thorough genetic analysis of the founding member of this novel family of DNA polymerases, TRF4. Analyses of mutants carrying 1 of 34 "surface-targeted" alanine scanning mutations in TRF4 have identified those regions required for Pol sigma's essential function, for its role in DNA double-strand break repair, and for its association with chromosomes. The data strongly support the importance of the regions of predicted structural similarity with the Pol beta superfamily as critical for Trf4p/Pol sigma's essential and repair functions. Surprisingly, five lethal mutations lie outside all polymerase homology in a C-terminal region. The protein possesses Mg2+-dependent 3' to 5' exonuclease activity. Cell cycle analysis reveals that Trf4p/Pol sigma associates with chromosomes in G1, S, and G2 phases, but that association is abolished coincident with dissolution of cohesion at the metaphase-to-anaphase transition.