The emergence of catalytically active RNA enzymes (ribozymes) is widely believed to have been an important transition in the origin of life. In the context of a likely heterogeneous chemical environment, substrate specificity and selectivity of these primordial enzymes would have been critical for function. Here we have explored the chemical fidelity, i.e. substrate selectivity and specificity for both single and multiple catalytic steps of the Z RNA polymerase ribozyme-a modern day analogue of the primordial RNA replicase. Using a wide range of nucleotide analogues and ionic conditions, we observe strong energetic but weak geometric discrimination at the incorporation step, indicative of an open active site. In contrast, stringent selectivity is exerted at the extension steps through specific down and upstream interactions with the 3′-terminal nucleoside as well as nascent product and template strands. Our results indicate specificity mechanisms that are found in functionally analogous forms in natural polymerases. They also reveal a level of chemical fidelity over multiple catalytic steps that is remarkable for a comparatively unoptimized enzyme developed de novo from a random sequence pool. The convergent evolution of specificity mechanisms in phylogenetically unrelated proteinaceous polymerases and polymerase ribozymes suggests that chemical as well as informational fidelity are emergent properties of polymerase enzymes.