Thirty years ago it was shown that the non-enzymatic, template-directed polymerization of activated mononucleotides proceeds readily in a homochiral system, but is severely inhibited by the presence of the opposing enantiomer1. This finding poses a severe challenge for the spontaneous emergence of RNA-based life, and has led to the suggestion that either RNA was preceded by some other genetic polymer that is not subject to chiral inhibition2 or chiral symmetry was broken through chemical processes before the origin of RNA-based life3, 4. Once an RNA enzyme arose that could catalyse the polymerization of RNA, it would have been possible to distinguish among the two enantiomers, enabling RNA replication and RNA-based evolution to occur. It is commonly thought that the earliest RNA polymerase and its substrates would have been of the same handedness, but this is not necessarily the case. Replicating D- and L-RNA molecules may have emerged together, based on the ability of structured RNAs of one handedness to catalyse the templated polymerization of activated mononucleotides of the opposite handedness. Here we develop such a cross-chiral RNA polymerase, using in vitro evolution starting from a population of random-sequence RNAs. The D-RNA enzyme, consisting of 83 nucleotides, catalyses the joining of L-mono- or oligonucleotide substrates on a complementary L-RNA template, and similar behaviour occurs for the L-enzyme with D-substrates and a D-template. Chiral inhibition is avoided because the 106-fold rate acceleration of the enzyme only pertains to cross-chiral substrates. The enzyme’s activity is sufficient to generate full-length copies of its enantiomer through the templated joining of 11 component oligonucleotides.