Humans are strongly lateralized for manual gestures at both individual and population levels. In contrast, the laterality bias in primates is less strong, leading some to suggest that lateralization evolved after the Pan and Homo lineages diverged. However, laterality in humans is also context-dependent, suggesting that observed differences in lateralization between primates and humans may be related to external factors such as the complexity of the social environment. Here we address this question in wild chimpanzees and examine the extent to (...) which the laterality of manual gestures is associated with social complexity. Right-handed gestures were more strongly associated with goal-directed communication such as repair through elaboration in response to communication failure than left-handed gestures. Right-handed gestures occurred in evolutionarily urgent contexts such as in interactions with central individuals in the network, including grooming reciprocity and mating, whereas left-handed gestures occurred in less-urgent contexts, such as travel and play. Right-handed gestures occurred in smaller parties and in the absence of social competition relative to left-handed gestures. Right-handed gestures increased the rate of activities indicating high physiological arousal in the recipient, whereas left-handed gestures reduced it. This shows that right- and left-handed gestures differ in cognitive and social complexity, with right-handed gestures facilitating more complex interactions in simpler social settings, whereas left-handed gestures facilitate more rewarding interactions in complex social settings. Differences in laterality between other primates and humans are likely to be driven by differences in the complexity of both the cognitive skills underpinning social interactions and the social environment. (shrink)