We present an approach to annotating timelines in stories where events are linked together by temporal relations into a temporal dependency tree. This approach avoids the disconnected timeline problems of prior work, and results in timelines that are more suitable for temporal reasoning. We show that annotating timelines as temporal dependency trees is possible with high levels of inter-annotator agreement - Krippendorff's Alpha of 0.822 on selecting event pairs, and of 0.700 on selecting temporal relation labels - even with the moderately sized relation set of BEFORE, AFTER, INCLUDES, IS-INCLUDED, IDENTITY and OVERLAP. We also compare several annotation schemes for identifying story events, and show that higher inter-annotator agreement can be reached by focusing on only the events that are essential to forming the timeline, skipping words in negated contexts, modal contexts and quoted speech.