Cumulative culture is rare, if not altogether absent in nonhuman species. At the foundation of cumulative learning is the ability to modify, relinquish, or build upon previous behaviors flexibly to make them more productive or efficient. Within the primate literature, a failure to optimize solutions in this way is often proposed to derive from low-fidelity copying of witnessed behaviors, suboptimal social learning heuristics, or a lack of relevant sociocognitive adaptations. However, humans can also be markedly inflexible in their behaviors, perseverating with, or becoming fixated on, outdated or inappropriate responses. Humans show differential patterns of flexibility as a function of cognitive load, exhibiting difficulties with inhibiting suboptimal behaviors when there are high demands on working memory. We present a series of studies on captive chimpanzees that indicate that behavioral conservatism in apes may be underlain by similar constraints: Chimpanzees showed relatively little conservatism when behavioral optimization involved the inhibition of a well-established but simple solution, or the addition of a simple modification to a well-established but complex solution. In contrast, when behavioral optimization involved the inhibition of a well-established but complex solution, chimpanzees showed evidence of conservatism. We propose that conservatism is linked to behavioral complexity, potentially mediated by cognitive resource availability, and may be an important factor in the evolution of cumulative culture.