Biology relies almost exclusively on homochiral building blocks to drive the processes of life. Yet cross-chiral interactions can occur between macromolecules of the opposite handedness, including a previously described polymerase ribozyme that catalyzes the template-directed synthesis of enantio-RNA. The present study sought to optimize and generalize this activity, employing in vitro evolution to select cross-chiral polymerases that use either mono- or trinucleotide substrates that are activated as the 5'-triphosphate. There was only modest improvement of the former activity, but dramatic improvement of the latter, which enables the trinucleotide polymerase to react 102-103-fold faster than its ancestor and to accept substrates with all possible sequence combinations. The evolved ribozyme can assemble long RNAs from a mixture of trinucleotide building blocks, including a two-fragment form of the ancestral polymerase ribozyme. Further improvement of this activity could enable the generalized cross-chiral replication of RNA, which would establish a new paradigm for the chemical basis of Darwinian evolution.