T4 polynucleotide kinase/phosphatase (Pnkp) exemplifies a family of bifunctional enzymes with 5'-kinase and 3' phosphatase activities that function in nucleic acid repair. T4 Pnkp is a homotetramer of a 301-aa polypeptide, which consists of an N-terminal kinase domain of the P-loop phosphotransferase superfamily and a C-terminal phosphatase domain of the DxD acylphosphatase superfamily. The homotetramer is formed via pairs of phosphatase-phosphatase and kinase-kinase homodimer interfaces. Here we identify four side chains-Asp187, Ser211, Lys258, and Asp277-that are required for 3' phosphatase activity. Alanine mutations at these positions abolished phosphatase activity without affecting kinase function or tetramerization. Conservative substitutions of asparagine or glutamate for Asp187 did not revive the 3' phosphatase, nor did arginine or glutamine substitutions for Lys258. Threonine in lieu of Ser211 and glutamate in lieu of Asp277 restored full activity, whereas asparagine at position 277 had no salutary effect. We report a 3.0 A crystal structure of the Pnkp tetramer, in which a sulfate ion is coordinated between Arg246 and Arg279 in a position that we propose mimics one of the penultimate phosphodiesters (5'NpNpNp-3') of the polynucleotide 3'-PO(4) substrate. The amalgam of mutational and structural data engenders a plausible catalytic mechanism for the phosphatase that includes covalent catalysis (via Asp165), general acid-base catalysis (via Asp167), metal coordination (by Asp165, Asp277 and Asp278), and transition state stabilization (via Lys258, Ser211, backbone amides, and the divalent cation). Other critical side chains play architectural roles (Arg176, Asp187, Arg213, Asp254). To probe the role of oligomerization in phosphatase function, we introduced six double-alanine cluster mutations at the phosphatase-phosphatase domain interface, two of which (R297A-Q295A and E292A-D300A) converted Pnkp from a tetramer to a dimer and ablated phosphatase activity.