A study was published in Nature examining communication among chimpanzees. It found that chimps use "words," and can combine the words into "syntactic-like structures," the beginnings of phrases / sentences.
"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.
So chimps have a "word" for surprise/danger and a "word" for come quickly, and when they combine them when seeing a snake, they are forming a proto-sentence with the approximate meaning of "Holy crap, get over here!"
To test this, the researchers surprised chimps with snake toys (models), which must have been fun, and found that other chimps frequently came to the caller when the "alarm-huu + waa-bark" combination was called. Then they played tapes of the "alarm-huu + waa-bark," the "alarm-huu" alone, and the "waa-bark" alone, and found that chimps were more responsive to the combination.
"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."
hat tip: @ed_hagen