We present a novel representation, evaluation measure, and supervised models for the task of identifying the multiword expressions (MWEs) in a sentence, resulting in a lexical semantic segmentation . Our approach generalizes a standard chunking representation to encode MWEs containing gaps, thereby enabling efficient sequence tagging algorithms for feature-rich discriminative models. Experiments on a new dataset of English web text offer the first linguistically-driven evaluation of MWE identification with truly heterogeneous expression types. Our statistical sequence model greatly outperforms a lookup-based segmentation procedure, achieving nearly 60% F 1 for MWE identification.