Disfluencies is an under-studied topic in NLP, even though it is ubiquitous in human conversation. This is largely due to the lack of datasets containing disfluencies. In this paper, we present a new challenge question answering dataset, Disfl-QA, a derivative of SQuAD, where humans introduce contextual disfluencies in previously fluent questions. Disfl-QA contains a variety of challenging disfluencies that require a more comprehensive understanding of the text than what was necessary in prior datasets. Experiments show that the performance of existing state-of-the-art question answering models degrades significantly when tested on Disfl-QA in a zero-shot setting. We show data augmentation methods partially recover the loss in performance and also demonstrate the efficacy of using gold data for fine-tuning. We argue that we need large-scale disfluency datasets in order for NLP models to be robust to them. The dataset is publicly available at: https://github.com/google-research-datasets/disfl-qa.