English news headlines form a register with unique syntactic properties that have been documented in linguistics literature since the 1930s. However, headlines have received surprisingly little attention from the NLP syntactic parsing community. We aim to bridge this gap by providing the first news headline corpus of Universal Dependencies annotated syntactic dependency trees, which enables us to evaluate existing state-of-the-art dependency parsers on news headlines. To improve English news headline parsing accuracies, we develop a projection method to bootstrap silver training data from unlabeled news headline-article lead sentence pairs. Models trained on silver headline parses demonstrate significant improvements in performance over models trained solely on gold-annotated long-form texts. Ultimately, we find that, although projected silver training data improves parser performance across different news outlets, the improvement is moderated by constructions idiosyncratic to outlet.