Chomsky does describe himself as a communist.

From Wikipedia, quoting Chomsky's 1976 interview with Peter Jay

Chomsky describes himself as a " libertarian socialist or anarcho-syndicalist or communist anarchist, in the tradition of, say, Bakunin and Kropotkin and others. They had in mind a highly organized form of society, but a society that was organized on the basis of organic units, organic communities. And generally, they meant by that the workplace and the neighborhood, and from those two basic units there could derive through federal arrangements a highly integrated kind of social organization which might be national or even international in scope. And these decisions could be made over a substantial range, but by delegates who are always part of the organic community from which they come, to which they return, and in which, in fact, they live."