From what I've heard, language is unambiguously unique to humans, if you consider grammar an integral part of languages. You can teach chimpanzees hand signs, but they could never make the leap to stringing them together under a coherent rule: something like the difference between "Mom give me cookies" vs "I give mom cookies."
(I'm no expert, so take that with a grain of salt.)
(I'm no expert, so take that with a grain of salt.)