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Language models are an important component of speech recognition. They aim to predict the probability of any word sequence. Traditional n-gram language models consider only adjacent lexical dependencies and so ignore longer-spanning dependencies. One might capture these long-spanning dependencies by augmenting traditional models with head-dependency information. A head word is the critical element in a phrase. Dependents modify the head. Prior research has shown that head-dependency relationships acquired from an annotated corpus can improve n-gram models. We propose a probabilistic parser and language model which incorporate head-dependency relationships obtained from the unsupervised algorithm in [10]. Preliminary information theoretic measures suggest that a model which combines n-grams and unsupervised head-dependencies will outperform tra-ditional n-gram models. We describe a probabilistic model. We discuss the algorithms and data structures neces-sary to implement the model efficiently in a chart parser. We also outline strategies for pruning and reestimation. Our results reveal that the automatically acquired head-depen