Most proteins associate into multimeric complexes with specific architectures, which often have functional properties like cooperative ligand binding, allosteric regulation, or the capacity to perform mechanical work. We have no detailed knowledge of how any multimer and its functions arose during historical evolution. Here we use ancestral protein reconstruction and biophysical assays to dissect the evolutionary origins of vertebrate hemoglobin (Hb), a heterotetramer of paralogous α and β subunits, which mediates oxygen transport and exchange...