We describe an approach to Grammatical Error Correction (GEC) that is effective at making use of models trained on large amounts of weakly supervised bitext. We train the Transformer sequence-to-sequence model on 4B tokens of Wikipedia revisions and employ an iterative decoding strategy that is tailored to the loosely-supervised nature of the Wikipedia training corpus. Finetuning on the Lang-8 corpus and ensembling yields an F0.5 of 58.3 on the CoNLL14 benchmark and a GLEU of 62.4 on JFLEG. The combination of weakly supervised training and iterative decoding obtains an F0.5 of 48.2 on CoNLL14 even without using any labeled GEC data.