The roles of chance, contingency, and necessity in evolution is unresolved, because they have never been assessed in a single system or on timescales relevant to historical evolution. We combined ancestral protein reconstruction and a new continuous evolution technology to mutate and select B-cell-lymphoma-2-family proteins to acquire protein-protein-interaction specificities that occurred during animal evolution. By replicating evolutionary trajectories from multiple ancestral proteins, we found that contingency generated over long historical timescales steadily erased necessity and overwhelmed chance as the primary cause of acquired sequence variation; trajectories launched from phylogenetically distant proteins yielded virtually no common mutations, even under strong and identical selection pressures. Chance arose because many sets of mutations could alter specificity at any timepoint; contingency arose because historical substitutions changed these sets. Our results suggest that patterns of variation in BCL-2 sequences – and likely other proteins, too – are idiosyncratic products of a particular, unpredictable course of historical events.