Arabic dialects present many challenges for machine translation, not least of which is the lack of data resources. We use crowdsourcing to cheaply and quickly build Levantine- English and Egyptian-English parallel corpora, consisting of 1.1M words and 380k words, respectively. The dialect sentences are selected from a large corpus of Arabic web text, and translated using Mechanical Turk. We use this crowdsourced data to build Dialect Arabic MT systems. Small amounts of dialect data have a dramatic impact on the quality of translation. When translating Egyptian and Levantine test sets, our Dialect Arabic MT system performs 6.3 and 7.0 BLEU points higher than a Modern Standard Arabic MT system trained on a 150 million word Arabic- English parallel corpus.