One of the most controversial hypotheses in cognitive science is the Chomskyan evolutionary conjecture that language arose instantaneously in humans through a single mutation. Here we analyze the evolutionary dynamics implied by this hypothesis, which has never been formalized before. The hypothesis supposes the emergence and fixation of a single mutant (capable of the syntactic operation Merge) during a narrow historical window as a result of frequency-independent selection under a huge fitness advantage in a population of an effective size no larger than ~15 000 individuals. We examine this proposal by combining diffusion analysis and extreme value theory to derive a probabilistic formulation of its dynamics. We find that although a macro-mutation is much more likely to go to fixation if it occurs, it is much more unlikely a priori than multiple mutations with smaller fitness effects. The most likely scenario is therefore one where a medium number of mutations with medium fitness effects accumulate. This precise analysis of the probability of mutations occurring and going to fixation has not been done previously in the context of the evolution of language. Our results cast doubt on any suggestion that evolutionary reasoning provides an independent rationale for a single-mutant theory of language.