Communicative skills of chimpanzees are of significant interest across many domains, such as developmental psychology (how does communication emerge in prelinguistic beings?), evolution (e.g., did human language evolve from primate gestures?), and in comparative psychology (how does the nonverbal communication of chimpanzees and humans compare?). Here we ask about how gestures develop in chimpanzee infants (n = 16) that were raised in an interactive program designed to study skill development. Data on socio-communicative development were collected following 4 hr of daily interaction with each infant, longitudinally from birth through the first year of life. A consistent and significant developmental pattern was found across the contexts of tickle play, grooming, and chase play: Infant chimpanzees first engaged in interactions initiated by others, then they initiated interactions, and finally, they requested others to join them in the interaction. Gestures were documented for initiating and requesting tickle play, for initiating and requesting grooming, and for initiating and requesting chase play. Gestural requests emerged significantly later than gestural initiations, but the age at which gestures emerged was significantly different across contexts. Those gestures related to hierarchical rank relations, that is, gestures used by subordinates in interaction with more dominant individuals, such as wrist presenting and rump presenting, did not emerge in the same manner as the other gestures. This study offers a new view on the development of gestures, specifically that many develop through interaction and communicate socio-emotional desires, but that not all gestures emerge in the same manner.