Neural Machine Translation (NMT) systems are known to degrade when confronted with noisy data, especially when the system is trained only on clean data. In this paper, we show that augmenting training data with sentences containing artificially-introduced grammatical errors can make the system more robust to such errors. In combination with an automatic grammar error correction system, we can recover 1.0 BLEU out of 2.4 BLEU lost due to grammatical errors. We also present a set of Spanish translations of the JFLEG grammar error correction corpus, which allows for testing NMT robustness to real grammatical errors.