The Optional Infinitive hypothesis proposed by Wexler (1994) is a theory of children’s early grammatical development that can be used to explain a variety of phenomena in children’s early multi-word speech. However, Wexler’s theory attributes a great deal of abstract knowledge to the child on the basis of rather weak empirical evidence. In this paper we present a computational model of early grammatical development which simulates Optional Infinitive phenomena as a function of the interaction between a performance-limited distributional analyser and the statistical properties of the input. Our findings undermine the claim that Optional Infinitive phenomena require an abstract grammatical analysis