Human intellect is characterized by intercorrelated psychological domains, including intelligence, academic performance and personality. Higher openness is associated with higher intelligence and better academic performance, yet high performance among individuals is itself attributable to intelligence, not openness. High conscientiousness individuals, although not necessarily more intelligent, are better performers. Work with other species is not as extensive, yet animals display similar relationships between exploration- and persistence-related personality traits and performance on cognitive tasks. However, previous studies linking cognition and personality have not tracked learning, performance and dropout over time—three crucial elements of cognitive performance. We conducted three participatory experiments with touchscreen cognitive tasks among 19 zoo-housed chimpanzees, whose personalities were assessed 3 years prior to the study. Performance and participation were recorded across experiments. High conscientiousness chimpanzees participated more, dropped out less and performed better, but their performance could be explained by their experience with the task. High openness chimpanzees tended to be more interested, perform better and continue to participate when not rewarded with food. Our results demonstrate that chimpanzees, like humans, possess broad intellectual capacities that are affected by their personalities.