Through syntax, i.e., the combination of words into larger phrases, language can express a limitless number of messages. Data in great apes, our closest-living relatives, are central to the reconstruction of syntax’s phylogenetic origins, yet are currently lacking. Here, we provide evidence for syntactic-like structuring in chimpanzee communication. Chimpanzees produce “alarm-huus” when surprised and “waa-barks” when potentially recruiting conspecifics during aggression or hunting. Anecdotal data suggested chimpanzees combine these calls specifically when encountering snakes. Using snake presentations, we confirm call combinations are produced when individuals encounter snakes and find that more individuals join the caller after hearing the combination. To test the meaning-bearing nature of the call combination, we use playbacks of artificially-constructed call combinations and both independent calls. Chimpanzees react most strongly to call combinations, showing longer looking responses, compared with both independent calls. We propose the “alarm-huu + waa-bark” represents a compositional syntactic-like structure, where the meaning of the call combination is derived from the meaning of its parts. Our work suggests that compositional structures may not have evolved de novo in the human lineage, but that the cognitive building-blocks facilitating syntax may have been present in our last common ancestor with chimpanzees.