The hypothesis that certain RNA molecules may be able to catalyse RNA replication is central to current theories of the early evolution of life. In support of this idea, we describe here an RNA that synthesizes RNA using the same reaction as that employed by protein enzymes that catalyse RNA polymerization. In the presence of the appropriate template RNA and nucleoside triphosphates, the ribozyme extends an RNA primer by successive addition of up to six mononucleotides. The added nucleotides are joined to the growing RNA chain by 3',5'-phosphodiester linkages. The ribozyme shows marked template fidelity: extension by nucleotides complementary to the template is up to 1,000 times more efficient than is extension by mismatched nucleotides.