Well, in the big picture, Chomsky created an activity which keeps liguists very busy. His approach, however, has contributed very little to language engineering.
Do you mean specifically of human languages? Because Chomsky's approach has contributed pretty extensively to programming language engineering, as the foundation of parsing theory and the whole formal language hierarchy (context-free, context-sensitive, regular, etc.).
I do agree it's been less successful for its original intended purpose, but things often find new life, which seems okay.
Yes: the Chomsky hierarchy is a fundamental of computer science, one of the great intellectual achievements of humanity. And in that respect also important to AI.
Chomsky is incredibly strong on anything that does not require empirical data.
But UG has no legs and Chomsky's analysis of syntax has very limited applicability and after many many IOUs, pretty much no empirical claims have panned out in any significant way.
If you take away the application of those basic computer science concepts to language, you unfortunately take away most of what Chomsky has written regarding linguistics, psychology and AI. Because of the sheer volume of output, that leaves a number of contributions. My point is that it is necessary to be discriminating rather than making Chomsky into the Pope, as certain fields have done for some time.
