We introduce a novel computer implementation of the Unification-Space parser (Vosse & Kempen 2000) in the form of a localist neural network whose dynamics is based on interactive activation and inhibition. The wiring of the network is determined by Performance Grammar (Kempen & Harbusch 2003), a lexicalist formalism with feature unification as binding operation. While the network is processing input word strings incrementally, the evolving shape of parse trees is represented in the form of changing patterns of activation in nodes that code for syntactic properties of words and phrases, and for the grammatical functions they fulfill. The system is capable, at least in a qualitative and rudimentary sense, of simulating several important dynamic aspects of human syntactic parsing, including garden-path phenomena and reanalysis, effects of complexity (various types of clause embeddings), fault-tolerance in case of unification failures and unknown words, and predictive parsing (expectation-based analysis, surprisal effects). English is the target language of the parser described.