Animals that sustain high levels of aerobic activity under hypoxic conditions (e.g., birds that fly at high altitude) face the physiological challenge of jointly optimizing blood-O2 affinity for O2 loading in the pulmonary circulation and O2 unloading in the systemic circulation. At high altitude, this challenge is especially acute for small endotherms like hummingbirds that have exceedingly high mass-specific metabolic rates. Here we report an experimental analysis of hemoglobin (Hb) function in South American hummingbirds that revealed a positive correlation between Hb-O2 affinity and native elevation. Protein engineering experiments and ancestral-state reconstructions revealed that this correlation is attributable to derived increases in Hb-O2 affinity in highland lineages, as well as derived reductions in Hb-O2 affinity in lowland lineages. Site-directed mutagenesis experiments demonstrated that repeated evolutionary transitions in biochemical phenotype are mainly attributable to repeated amino acid replacements at two epistatically interacting sites that alter the allosteric regulation of Hb-O2 affinity. These results demonstrate that repeated changes in biochemical phenotype involve parallelism at the molecular level, and that mutations with indirect, second-order effects on Hb allostery play key roles in biochemical adaptation.