Manual gestures and speech recruit a common neural network, involving Broca’s area in the left hemisphere. Such speech-gesture integration gave rise to theories on the critical role of manual gesturing in the origin of language. Within this evolutionary framework, research on gestural communication in our closer primate relatives has received renewed attention for investigating its potential language-like features. Here, using in vivo anatomical MRI in 50 baboons, we found that communicative gesturing is related to Broca homologue’s marker in monkeys, namely the ventral portion of the Inferior Arcuate sulcus ( IA sulcus ). In fact, both direction and degree of gestural communication’s handedness – but not handedness for object manipulation are associated and correlated with contralateral depth asymmetry at this exact IA sulcus portion. In other words, baboons that prefer to communicate with their right hand have a deeper left-than-right IA sulcus , than those preferring to communicate with their left hand and vice versa. Interestingly, in contrast to handedness for object manipulation, gestural communication’s lateralisation is not associated to the Central sulcus depth asymmetry, suggesting a double dissociation of handedness’ types between manipulative action and gestural communication. It is thus not excluded that this specific gestural lateralisation signature within the baboons’ frontal cortex might reflect a phylogenetical continuity with language-related Broca lateralisation in humans.