Chomsky did make some very important contributions to CS with his theories on grammars, but as I like to point out, John Backus was working on virtually the same thing at virtually the same time, to the point where it's not at all unreasonable to say that he independently discovered much of what Chomsky did.
I'm not sure that the failures of AI are really traceable to Chomsky, though - I think it's more that the problem has turned out to be much deeper and harder than anyone originally thought it would be. Really, nobody, IMO, has adequately framed the "problem" of artificial intelligence, let alone "solved" it.
I've been away all day and am a bit surprised to have gotten by with so few flames. I came upon Chomsky from the psychology/learning theory aspect rather than from the computer science or political aspect of his writings. this was about 35 years ago and I have not kept up with the details of his career.
It seemed to me that his assertion that aspects of language were built in to the brain was tautalogical -- of course there must be some underlying structural differences between humans, apes, and other animals -- else we could teach sign language or reading to dogs. The question is whether this assertion adds anything to our knowledge. It seems to me that transformational grammer has been kind of sterile in the realm of human language. I know of no school of psychology that uses any of his ideas in a teaching or therapy setting. I know of no Chomskian school of literary criticism, no transformational grammer of poetry.
The reason, I assume, is that grammer and syntax are rather trivial aspects on language that say nothing about the underlying motivation for talking in the first place. Is there, for example, a Chomskian method for analyzing a statement for its probable truthfulness or sincerity, or humorous intent, or double entendre? Is there a Chomskian analysis of inflection?
I see a parallel in Chomsky's approach to language and his approach to politics. I politics he believes that all human needs can be fulfilled by the application of rigorous logic (from above, of course). Individual will is messy and unnecessary. Emotions are nasty and need to be suppressed.