The idea that the first living systems on earth were based on self-replicating RNA molecules has recently become popular as a result of the discovery of ribozymes. However, there are several major problems associated with the prebiotic synthesis of ribonucleotides. In addition, there is the newly recognized problem of enantiomeric cross-inhibition, whereby template-directed polymerization involving one enantiomer of RNA is inhibited strongly by the presence of the other enantiomer. Here we propose that RNA was preceded in the evolution of life by a polymer constructed from flexible, acyclic, probably prochiral nucleotide analogues that were synthesized readily on the primitive earth. Several potentially prebiotic nucleotide analogues are considered in this context, and some of the consequences of this proposal are discussed.