Modern text classification models are susceptible to adversarial examples, perturbed versions of the original text indiscernible by humans which get misclassified by the model. Recent works in NLP use rule-based synonym replacement strategies to generate adversarial examples. These strategies can lead to out-of-context and unnaturally complex token replacements, which are easily identifiable by humans. We present BAE, a black box attack for generating adversarial examples using contextual perturbations from a BERT masked language model. BAE replaces and inserts tokens in the original text by masking a portion of the text and leveraging the BERT-MLM to generate alternatives for the masked tokens. Through automatic and human evaluations, we show that BAE performs a stronger attack, in addition to generating adversarial examples with improved grammaticality and semantic coherence as compared to prior work.