Chomsky's notion of Universal Grammar presupposed that (1) there are universal syntactic features that can only be accounted for by an innate faculty and (2) language acquisition depended an such an innate faculty.
Many linguists disagree with this account. First, infants have a significant capacity to learn non-linguistic and well as linguistic information, and thus acquisition of language need not be a special case. Second, children raised with no contact with language are incapable of learning language later in life, thus making its innateness suspect. Third, language appears not to be a uniquely human characteristic, as Chomsky theorized.
Finally, there is a problem of circular definition, in that for Chomsky, to be called a language something must contain certain syntactic features; this means that anything not containing those features would not be a language (according to Chomsky). This does not prove anything about language itself but rather about how linguists define languages.