RNA loops that adopt a characteristic GNRA "tetraloop" fold are common in natural RNAs. Here, we have used in vitro selection by means of mRNA-peptide fusions to select peptides that bind an example of this RNA loop motif. Starting with the RNA recognition domain from the lambda N protein, we have constructed libraries containing 150, 1,600, and 9 trillion different peptide sequences as mRNA-peptide fusions and isolated those capable of high-affinity RNA binding. These selections have resulted in more than 80 different peptides that bind the same RNA loop. The highest affinity peptides exhibit low nanomolar dissociation constants as well as the ability to discriminate RNA hairpins differing by a single loop nucleotide. Thus, our work demonstrates that numerous, chemically distinct solutions exist for a particular RNA recognition problem.