Infections with viral pathogens impose considerable selective pressure on host defensive genes. Those genes at the forefront, responsible for identifying and binding exogenous molecular viral components, will carry the hallmarks of this struggle. Oligoadenylate synthetase (OAS) enzymes play a major role in the innate defense against a large number of viruses by acting as sensors of viral infections. Following their up-regulation by the interferon pathway, OASs bind viral dsRNA and then signal ribonuclease L (RNase L) to degrade RNA, shutting down viral and host protein synthesis. We have investigated the evolution of OAS1 in twenty-two Old World monkey species. We identified a total of 35 codons with the earmarks of positive selection and we performed a comprehensive analysis of their functional significance using in silico modeling of the OAS1 protein. Subdividing OAS1 into functional domains revealed intense purifying selection in the active domain but significant positive directional selection in the RNA-binding domain (RBD), the region where OAS1 binds viral dsRNA. The modeling analysis revealed a concentration of rapidly evolving residues in one region of the RBD suggestive of the sub-functionalization of different regions of the RBD. This analysis also identified several positively selected residues circumscribing the entry to the active site suggesting adaptive evasion of viral antagonism and/or selection for production of oligoadenylate of different length.