All known polymerases copy genetic material by catalyzing phosphodiester bond formation. This highly conserved activity proceeds by a common mechanism, such that incorporated nucleoside analogs terminate chain elongation if the resulting primer strand lacks a terminal hydroxyl group. Even conservatively substituted 3′-amino nucleotides generally act as chain terminators, and no enzymatic pathway for their polymerization has yet been found. Although 3′-amino nucleotides can be chemically coupled to yield stable oligonucleotides containing N3′→P5′ phosphoramidate (NP) bonds, no such internucleotide linkages are known to occur in nature. Here, we report that 3′-amino terminated primers are, in fact, slowly extended by the DNA polymerase from B. stearothermophilus in a template-directed manner. When its cofactor is Ca2+ rather than Mg2+, the reaction is fivefold faster, permitting multiple turnover NP bond formation to yield NP-DNA strands from the corresponding 3′-amino-2′,3′-dideoxynucleoside 5′-triphosphates. A single active site mutation further enhances the rate of NP-DNA synthesis by an additional 21-fold. We show that DNA-dependent NP-DNA polymerase activity depends on conserved active site residues and propose a likely mechanism for this activity based on a series of crystal structures of bound complexes. Our results significantly broaden the catalytic scope of polymerase activity and suggest the feasibility of a genetic transition between native nucleic acids and NP-DNA.