Human communication has been described as a contextual social inference process. Research into great ape communication has been inspired by this view to look for the evolutionary roots of the social, cognitive, and interactional processes involved in human communication. This approach has been highly productive, yet it is often compromised by a too-narrow focus on how great apes use and understand individual signals. In this paper, we introduce a computational model that formalizes great ape communication as a multi-faceted social inference process that relies on information contained in the signal, the relationship between communicative partners, and the social context. This model makes accurate qualitative and quantitative predictions about real-world communicative interactions between semi-wild-living chimpanzees. When enriched with a pragmatic reasoning process, the model explains repeatedly reported differences between humans and great apes in the interpretation of ambiguous signals (e.g. pointing gestures). This approach has direct implications for observational and experimental studies of great ape communication and provides a new tool for theorizing about the evolution of uniquely human communication.