Neural machine translation systems typically are trained on curated corpora and break when faced with non-standard orthography or punctuation. Resilience to spelling mistakes and typos, however, is crucial as machine translation systems are used to translate texts of informal origins, such as chat conversations, social media posts and web pages. We propose a simple generative noise model to generate adversarial examples of ten different types. We use these to augment machine translation systems’ training data and show that, when tested on noisy data, systems trained using adversarial examples perform almost as well as when translating clean data, while baseline systems’ performance drops by 2-3 BLEU points. To measure the robustness and noise invariance of machine translation systems’ outputs, we use the average translation edit rate between the translation of the original sentence and its noised variants. Using this measure, we show that systems trained on adversarial examples on average yield 50 % consistency improvements when compared to baselines trained on clean data.