A shortened form of the self-splicing ribosomal RNA intervening sequence of Tetrahymena thermophila has enzymatic activity as a poly(cytidylic acid) polymerase [Zaug, A.J. & Cech, T.R. (1986) Science 231, 470-475]. Based on the known properties of this enzyme, a detailed model is developed for the template-dependent synthesis of RNA by an RNA polymerase itself made of RNA. The monomer units for RNA synthesis are tetra- and pentanucleotides of random base sequence. Polymerization occurs in a 5'-to-3' direction, and elongation rates are expected to approach two residues per minute. If the RNA enzyme could use another copy of itself as a template, RNA self-replication could be achieved. Thus, it seems possible that RNA catalysts might have played a part in prebiotic nucleic acid replication, prior to the availability of useful proteins.