Threose nucleic acid (TNA) is an unnatural genetic polymer capable of undergoing Darwinian evolution to generate folded molecules with ligand-binding activity. This property, coupled with a nuclease-resistant backbone, makes TNA an attractive candidate for future applications in biotechnology. Previously, we have shown that an engineered form of the Archaean replicative DNA polymerase 9°N, known commercially as Therminator DNA polymerase, can copy a three-letter genetic alphabet (A,T,C) from DNA into TNA. However, our ability to transcribe four-nucleotide libraries has been limited by chain termination events that prevent the synthesis of full-length TNA products. Here, we show that chain termination is caused by tG:dG mispairing in the enzyme active site. We demonstrate that the unnatural base analogue 7-deazaguanine (7dG) will suppress tGTP misincorporation by inhibiting the formation of Hoogsteen tG:dG base pairs. DNA templates that contain 7dG in place of natural dG residues replicate with high efficiency and >99% overall fidelity. Pre-steady-state kinetic measurements indicate that the rate of tCTP incorporation is 5-fold higher opposite 7dG than dG and only slightly lower than dCTP incorporation opposite either 7dG or dG. These results provide a chemical solution to the problem of how to synthesize large, unbiased pools of TNA molecules by polymerase-mediated synthesis.