In this paper we present a new class of language models. This class derives from link grammar, a context-free formalism for the description of natural language. We describe an algorithm for determining maximum-likelihood estimates of the parameters of these models. The language models which we present differ from previous models based on stochastic context-free grammars in that they are highly lexical. In particular, they include the familiar n-gram models as a natural subclass. The motivation for considering this class is to estimate the contribution which grammar can make to reducing the relative entropy of natural language.