The RNA World model for prebiotic evolution posits the selection of catalytic/template RNAs from random populations. The mechanisms by which these random populations could be generated de novo are unclear. Non-enzymatic and RNA-catalyzed nucleic acid polymerizations are poorly processive, which means that the resulting short-chain RNA population could contain only limited diversity. Nonreciprocal recombination of smaller RNAs provides an alternative mechanism for the assembly of larger species with concomitantly greater structural diversity; however, the frequency of any specific recombination event in a random RNA population is limited by the low probability of an encounter between any two given molecules. This low probability could be overcome if the molecules capable of productive recombination were redundant, with many nonhomologous but functionally equivalent RNAs being present in a random population. Here we report fluctuation experiments to estimate the redundancy of the set of RNAs in a population of random sequences that are capable of non-Watson-Crick interaction with another RNA. Parallel SELEX experiments showed that at least one in 10(6) random 20-mers binds to the P5.1 stem-loop of Bacillus subtilis RNase P RNA with affinities equal to that of its naturally occurring partner. This high frequency predicts that a single RNA in an RNA World would encounter multiple interacting RNAs within its lifetime, supporting recombination as a plausible mechanism for prebiotic RNA evolution. The large number of equivalent species implies that the selection of any single interacting species in the RNA World would be a contingent event, i.e., one resulting from historical accident.