Interactions among mutations within a protein have the potential to make molecular evolution contingent and irreversible, but the extent to which epistasis actually shaped historical evolutionary trajectories is unclear. We addressed this question by identifying all amino acid substitutions that occurred during the billion-year evolutionary history of the heat shock protein 90 (Hsp90) ATPase domain beginning from a deep eukaryotic ancestor to modern Saccharomyces cerevisiae and then precisely measuring their fitness effects when introduced into both extant and reconstructed ancestral Hsp90 proteins. We find a pervasive influence of epistasis: of 98 derived states that evolved during history, most were deleterious at times before they happened, and the vast majority also became subsequently entrenched, with the ancestral state becoming deleterious after its substitution. This epistasis was primarily caused by specific interactions among sites rather than a general permissive or restrictive effect on the protein's tolerance to mutation. Our results show that epistasis continually opens and closes windows of mutational opportunity over evolutionary timescales, producing histories and biological states that reflect the transient internal constraints imposed by a protein's fleeting sequence states.