Roughly 10% of all known enzyme structures have an alpha/beta barrel domain. The members of this large family of proteins catalyze very different types of reactions. Such diversity of function has made this family a target for protein engineering. The evolutionary history of this family has been the subject of vigorous debate. In this paper, arguments are made to support the divergence of all members of this family from a common ancestor. Because of the lack of strong sequence homology, the ancestral molecule must be very old. A hypothesis concerning the relationship between chemical mechanism and evolutionary history is discussed. Evidence is presented to suggest that convergent molecular evolution occurs when there is only one energetically reasonable pathway for a chemical reaction.