Recombination, the exchange of information between different genetic polymer strands, is of fundamental importance in biology for genome maintenance and genetic diversification mediated by dedicated recombinase enzymes. Here, we describe a pervasive non-enzymatic capacity for recombination (and ligation) in random-sequence genetic oligomer pools. Specifically, we examine random and semi-random eicosamer (N20) pools of RNA, DNA and the unnatural genetic polymers ANA (arabino-), HNA (hexitol-) and AtNA (altritol-nucleic acids). While DNA, ANA and HNA pools proved inert, RNA and AtNA pools displayed diverse modes of spontaneous intermolecular recombination, connecting recombination mechanistically to the vicinal ring cis-diol configuration shared by RNA and AtNA. Thus, the chemical constitution that renders both susceptible to hydrolysis emerges as the fundamental determinant of an innate capacity for recombination, which is shown to enable a concomitant increase in compositional, informational and structural pool complexity and hence evolutionary potential.