A critical event in the origin of life is thought to have been the emergence of an RNA molecule capable of replicating a primordial RNA "genome." Here we describe the evolution and engineering of an RNA polymerase ribozyme capable of synthesizing RNAs of up to 95 nucleotides in length. To overcome its sequence dependence, we recombined traits evolved separately in different ribozyme lineages. This yielded a more general polymerase ribozyme that was able to synthesize a wider spectrum of RNA sequences, as we demonstrate by the accurate synthesis of an enzymatically active RNA, a hammerhead endonuclease ribozyme. This recapitulates a central aspect of an RNA-based genetic system: the RNA-catalyzed synthesis of an active ribozyme from an RNA template.