A remarkable feature of human handedness at the population level is specialization of the hands, the right hand performing usually better than the left. This specialization might have an evolutionary advantage, because it provides the individual and population with a wider range of skill. We therefore investigated the relationships between hand skill asymmetry and potential markers of Darwinian fitness that have been hypothesized to explain the bias in hand preference: creativity, aggression and developmental and health problems. Over twenty thousand participants (56% left-handers) completed an online survey, including a finger-tapping task to measure hand skill asymmetry. Left-skilled individuals were overall more aggressive than right-skilled individuals and rated themselves as more artistically creative. However, when assessed with a questionnaire, they were less creative on problem solving and equally artistically creative compared to right-skilled individuals, who reported more health problems. Conclusion: we found some evidence for current selection on the direction of lateralization of hand skill although the effect sizes were rather low. Strength of lateralization of hand skill showed only a few associations with fitness proxies. We suggest that Darwinian selection on hand preference (Zickert, Feen, van der, Geuze, & Groothuis, 2018. Fitness costs and benefits associated with hand preference in humans: A large internet study in a Dutch sample. Evolution and Human Behavior, 39, 235-248) and hand skill asymmetry (present study) may be attenuated in modern society.