Theories of language evolution depend in part upon accurate empirical and comparative assessment of animal communicative capacities. One problem, demonstrated by recent discoveries, is that we still do not know how complex animal communication is. Ontogenetic analyses are helping to change this. Only one natural communication system is considered combinatorially complex with respect to mapping complex structure to complex meaning. This is human language. With a limited sound set, we combine words into utterances, generating endless new and relational meanings. Most animals have a limited sound set that is largely fixed from birth, and per species produce few multi-signal utterances in which the meaning shifts compared to the composing signals. However, recent studies delving into vocal sequence production suggest a dramatically different pattern in chimpanzee vocal production. Chimpanzees demonstrate highly flexible abilities to combine calls with ordering and recombinatorial properties. Vocal combinations which show compositional-like structures, such that calls combined into utterances may disambiguate, add or generate new meanings compared to the composing calls. Like humans but unlike African monkeys, ontogenetic development is protracted, with utterance length and diversity dramatically increasing until 10 years of age. Such a developmental trajectory, in combination with population differences documented in sequence structure, are both suggestive of social learning capacities. Social learning is also indicated by population and community differences in the form and usage of some gestural signals. Taken together, our results place chimpanzee combinatorial capacities between those of humans and African monkeys, with implications for brain evolution, including changes to reorganization of human language tract homologues and for evolution of language theories.