This paper describes a computational model which simulates the change in the use of optional infinitives that is evident in children learning Dutch as their first language. The model, developed within the framework of MOSAIC, takes naturalistic, child directed speech as its input, and analyses the distributional regularities present in the input. It slowly learns to generate longer utterances as it sees more input. We show that the developmental characteristics of Dutch children’s speech (with respect to optional infinitives) are a natural consequence of MOSAIC’s learning mechanisms and the gradual increase in the length of the utterances it produces. In contrast with Nativist approaches to syntax acquisition, the present model does not assume large amounts of innate knowledge in the child, and provides a quantitative process account of the development of optional infinitives.