While neural machine translation (NMT) achieves remarkable performance on clean, in-domain text, performance is known to degrade drastically when facing text which is full of typos, grammatical errors and other varieties of noise. In this work, we propose a multi-task learning algorithm for transformer-based MT systems that is more resilient to this noise. We describe our submission to the WMT 2019 Robustness shared task based on this method. Our model achieves a BLEU score of 32.8 on the shared task French to English dataset, which is 7.1 BLEU points higher than the baseline vanilla transformer trained with clean text.