Through an analysis of chimpanzee–human discourse, we show that two Pan troglodytes chimpanzees and two Pan paniscus chimpanzees (bonobos) exposed to a humanly devised symbol system use partial or complete repetition of others' symbols, as children do: they do not produce rote imitations, but instead use repetition to fulfil a variety of pragmatic functions in discourse. These functions include agreement, request, promise, excitement, and selection from alternatives. In so doing, the chimpanzees demonstrate contingent turn-taking and the use of simple devices for lexical cohesion. In short, they demonstrate conversational competence. Because of the presence of this conversational competence in three sibling species, chimpanzees, bonobos, and humans, it is concluded that the potential to express pragmatic functions through repetition was part of the evolutionary history of human language, present in our common ancestor before the phylogenetic divergence of hominids and chimpanzees. In the context of these similarities, two interesting differences appeared: (1) Human children sometimes used repetition to stimulate more talk in their conversational partner; the chimpanzees, in contrast, use repetition exclusively to forward the non-verbal action. This difference may illuminate a unique feature of human linguistic communication, or it may simply reflect a modality difference (visual symbols used by the chimpanzees, speech used by the children) in the symbol systems considered in this research. A second difference seems likely to reflect a true species difference: utterance length. The one- and two-symbol repetitions used by the chimpanzees to fulfil a variety of pragmatic functions were less than half the maximum length found in either the visual symbol combinations addressed to them by their adult human caregivers or the oral repetitions of two-year-old children. This species difference probably reflects the evolution of increased brain size and consequent increased memory capacity that has occurred since the phylogenetic divergence of hominids and chimpanzees four to seven million years ago.