We present a simple method for learning part-of-speech taggers for languages like Akawaio, Aukan, or Cakchiquel -- languages for which nothing but a translation of parts of the Bible exists. By aggregating over the tags from a few annotated languages and spreading them via word-alignment on the verses, we learn POS taggers for 100 languages, using the languages to bootstrap each other. We evaluate our cross-lingual models on the 25 languages where test sets exist, as well as on another 10 for which we have tag dictionaries. Our approach performs much better (20-30%) than state-of-the-art unsupervised POS taggers induced from Bible translations, and is often competitive with weakly supervised approaches that assume high-quality parallel corpora, representative monolingual corpora with perfect tokenization, and/or tag dictionaries. We make models for all 100 languages available.