We propose UDP, the first training-free parser for Universal Dependencies (UD). Our algorithm is based on PageRank and a small set of head attachment rules. It features two-step decoding to guarantee that function words are attached as leaf nodes. The parser requires no training, and it is competitive with a delexicalized transfer system. UDP offers a linguistically sound unsupervised alternative to cross-lingual parsing for UD, which can be used as a baseline for such systems. The parser has very few parameters and is distinctly robust to domain change across languages.