In his 1956 paper ‘Three Models for the Description of Language’ Noam Chomsky posed an interesting open question: when we consider the human languages purely as sets of strings of words (henceforth stringsets), do they always fall within the class called context-free languages (CFL’s)? Chomsky declared that he did not know the answer to this question, and turned to a very different set of questions concerning relative elegance and economy of different types of description. Since 1956 various authors (Chomsky included) have attempted to provide answers in the negative, and the negative answer is now the standardly accepted one. We take up the question again in this paper, and show that it is still open, as all the arguments for the negative answer that have been provided in the literature are either empirically or formally incorrect.