We present a neural-network-based statistical parser, trained and tested on the Penn Treebank. The neural network is used to estimate the parameters of a generative model of left-corner parsing, and these parameters are used to search for the most probable parse. The parser's performance (88.8% F-measure) is within 1% of the best current parsers for this task, despite using a small vocabulary size (512 inputs). Crucial to this success is the neural network architecture's ability to induce a finite representation of the unbounded parse history, and the biasing of this induction in a linguistically appropriate way.