"Kripke detects an entirely novel form of sceptical argument that allegedly establishes that there is no fact, either in my mind or in my external behaviour, that constitutes my meaning something by the words I utter, or that fixes what will count as a correct application of a rule that I grasp. The conclusion of his sceptical argument -- that no one can ever mean anything by their words, or be following a rule that fixes what counts as a correct or an incorrect application of it -- is clearly deeply paradoxical, and it is impossible that anyone should rest content with it."(Marie McGinn, Wittgenstein and the Philosophical Investigations, p. 75)
So, Chomsky argued that the number of possible languages a child would have to choose from is simply too large for there not to be a constraint on the possible syntactic structure the child actually selects from(otherwise the child would not be able to acquire language at all, especially as quickly as children do.) This seems to me to be his most powerful argument. As to what those structures are etc..., well that can be argued over forever. Wittgenstein's sceptical arguments about meaning and so on, have the feel of this kind of problem. If I'm reading all of this right, our uses of words do not sufficiently constrain their possible meaning and our definitions of rules are insufficiently 'fixing' of future use. A solution to this problem would be that there are certain structures underlying the use of language that render these problems solved, otherwise we couldn't communicate.