Dimeric proteins can arise by the swapping of structural domains between monomers. The prevalence of this occurrence is unknown. Ribonuclease A (RNase A) is assumed to be a monomer near physiological conditions. Here, this hypothesis is tested and found to be imprecise. The two histidine residues (His12 and His119) in the active site of RNase A arise from two domains (S-peptide and S-protein) of the protein. The H12A and H119A variants have 105-fold less ribonucleolytic activity than does the wild-type enzyme. Incubating a 1:1 mixture of the H12A and H119A variants at pH 6.5 and 65 °C results in a 103-fold increase in ribonucleolytic activity. A large quantity of active dimer can be produced by lyophilizing a 1:1 mixture of the H12A and H119A variants from acetic acid. At pH 6.5 and 65 °C, the ribonucleolytic activity of this dimer converges to that of the dimer formed by simply incubating the monomers, as expected for a monomer–dimer equilibrium. The equilibrium dissociation constant for the dimer is near 2 mM at both 65 and 37 °C. This value of Kd is only 20-fold greater than the concentration of RNase A in the cow pancreas, suggesting that RNase A dimers exist in vivo. The intrinsic ability of RNase A to form dimers under physiological conditions is consistent with a detailed model for the evolution of homodimeric proteins. Dimers of “monomeric” proteins could be more prevalent than is usually appreciated.