This research proposes and evaluates a linguistically motivated approach to extracting temporal structure from text. Pairs of events in a verb-clause construction were considered, where the first event is a verb and the second event is the head of a clausal argument to that verb. All pairs of events in the TimeBank that participated in verb-clause constructions were selected and annotated with the labels BEFORE, OVERLAP and AFTER. The resulting corpus of 895 event-event temporal relations was then used to train a machine learning model. Using a combination of event-level features like tense and aspect with syntax-level features like the paths through the syntactic tree, support vector machine (SVM) models were trained which could identify new temporal relations with 89.2% accuracy. High accuracy models like these are a first step towards automatic extraction of temporal structure from text.