Using novel advances in computational chemistry, we demonstrate that the set of 20 genetically encoded amino acids, used nearly universally to construct all coded terrestrial proteins, has been highly influenced by natural selection. We defined an adaptive set of amino acids as one whose members thoroughly cover relevant physico-chemical properties, or "chemistry space." Using this metric, we compared the encoded amino acid alphabet to random sets of amino acids. These random sets were drawn from a computationally generated compound library containing 1913 alternative amino acids that lie within the molecular weight range of the encoded amino acids. Sets that cover chemistry space better than the genetically encoded alphabet are extremely rare and energetically costly. Further analysis of more adaptive sets reveals common features and anomalies, and we explore their implications for synthetic biology. We present these computations as evidence that the set of 20 amino acids found within the standard genetic code is the result of considerable natural selection. The amino acids used for constructing coded proteins may represent a largely global optimum, such that any aqueous biochemistry would use a very similar set.