We propose and evaluate a linguistically motivated approach to extracting temporal structure necessary to build a timeline. We considered pairs of events in a verb-clause construction, where the first event is a verb and the second event is the head of a clausal argument to that verb. We selected all pairs of events in the TimeBank that participated in verb-clause constructions and annotated them 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, we were able to train a support vector machine (SVM) model which could identify new temporal relations with 89.2% accuracy. High accuracy models like these are a first step towards automatic extraction of timeline structures from text.