This thesis presents the first application of the state-of-the-art head-driven statistical parsing model of Collins (1999) as a simultaneous language model and parser for large-vocabulary speech recognition. The model is adapted to an online left to right chart-parser for word lattices, integrating acoustic, N-gram, and parser probabilities. The parser uses structural and lexical dependencies not considered by N-gram models, conditioning recognition on more linguistically-grounded relationships. By preferring paths through the word lattice for which a probable parse exists, word error rate can be reduced and important syntactic and semantic relationships can be determined in a single step process. New forms of heuristic search and pruning are employed to improve efficiency. Experiments on the Wall Street Journal treebank and lattice corpora show word error rates competitive with the standard N-gram language model while extracting additional structural information useful for speech understanding.