We describe a baseline dependency parsing system for the CoNLL2017 Shared Task. This system, which we call "ParseySaurus," uses the DRAGNN framework [Kong et al, 2017] to combine transition-based recurrent parsing and tagging with character-based word representations. On the v1.3 Universal Dependencies Treebanks, the new system outpeforms the publicly available, state-of-the-art "Parsey's Cousins" models by 3.47% absolute Labeled Accuracy Score (LAS) across 52 treebanks.