Does it mean learning words (whether gestural or vocal or written) for things? For actions? Does it involve combining them in prescribed (or consistent) ways for routine situations? Novel situations? Does it involve recursion, or creating novel words or word combinations?
Chickens can learn words. It's called "conditioning". You can teach sentences to some animals--they can't reproduce them, but they learn them. But it's almost certain that they're learning them as very, very long words--or, rather, enough of the beginning to disambiguate between sentences.
Nim was supposed to have innovated word combinations for novel items, to have had syntax. These are typically considered requirements for "language". Recursion is a definite plus, as well. Showing that Nim could parrot, or learn words for things, would have been a null result. The early claims--claims repeated for all sorts of different primate species, and members of those species, to this day--is that they have syntax, they can innovate so they don't just have words for things but words for features that can be abstracted away from a given object or class of objects.
Thing is, when you look at the video, the uncut video, all the claims pretty much disintegrated. Vickie Fromkin had at one such example, I forget which primate it was. There was a video, 20 or 30 minutes, "proving" that the ape/chimp/etc. had language. Upon digging, there were 700 hours of video that those 20-30 minutes were culled from. They made the same gestures in meaningless contexts; they mimicked things they had seen, which their trainers had overlooked; their syntax varied so much as to be non-existent. Some people cried foul, and were offended that the primate would be so disparaged; they were ignored or belittled, since challenging a result in science is what makes it science.
The most recent claims are that they don't have *those* aspects of language, but discourse pragmatics--they're sensitive to the context in which things are said, intonation. Such claims are hard to disprove. But I'm sure somebody will, if they care.
As for Chomsky ... there's the Chomskybot!
http://rubberducky.org/cgi-bin/chomsky.pl