Multiple lines of evidence support the hypothesis that the early evolution of life was dominated by RNA, which can both transfer information from generation to generation through replication directed by base-pairing, and carry out biochemical activities by folding into functional structures. To understand how life emerged from prebiotic chemistry we must therefore explain the steps that led to the emergence of the RNA world, and in particular, the synthesis of RNA. The generation of pools of highly pure ribonucleotides on the early Earth seems unlikely, but the presence of alternative nucleotides would support the assembly of nucleic acid polymers containing nonheritable backbone heterogeneity. We suggest that homogeneous monomers might not have been necessary if populations of heterogeneous nucleic acid molecules could evolve reproducible function. For such evolution to be possible, function would have to be maintained despite the repeated scrambling of backbone chemistry from generation to generation. We have tested this possibility in a simplified model system, by using a T7 RNA polymerase variant capable of transcribing nucleic acids that contain an approximately 11 mixture of deoxy- and ribonucleotides. We readily isolated nucleotide-binding aptamers by utilizing an in vitro selection process that shuffles the order of deoxy- and ribonucleotides in each round. We describe two such RNA/DNA mosaic nucleic acid aptamers that specifically bind ATP and GTP, respectively. We conclude that nonheritable variations in nucleic acid backbone structure may not have posed an insurmountable barrier to the emergence of functionality in early nucleic acids.