This paper introduces Mixat: a dataset of Emirati speech code-mixed with English. Mixat was developed to address the shortcomings of current speech recognition resources when applied to Emirati speech, and in particular, to bilignual Emirati speakers who often mix and switch between their local dialect and English. The data set consists of 15 hours of speech derived from two public podcasts featuring native Emirati speakers, one of which is in the form of conversations between the host and a guest. Therefore, the collection contains examples of Emirati-English code-switching in both formal and natural conversational contexts. In this paper, we describe the process of data collection and annotation, and describe some of the features and statistics of the resulting data set. In addition, we evaluate the performance of pre-trained Arabic and multi-lingual ASR systems on our dataset, demonstrating the shortcomings of existing models on this low-resource dialectal Arabic, and the additional challenge of recognizing code-switching in ASR. The dataset will be made publicly available for research use.