We present a new human-human dialogue dataset - PhotoChat, the first dataset that casts light on the photo sharing behavior in online messaging. PhotoChat contains 12k dialogues, each of which is paired with a user photo that is shared during the conversation. Based on this dataset, we propose two tasks to facilitate research on image-text modeling: a photo-sharing intent prediction task that predicts whether one intends to share a photo in the next conversation turn, and a photo retrieval task that retrieves the most relevant photo according to the dialogue context. In addition, for both tasks, we provide baseline models using the state-of-the-art models and report their benchmark performances. The best image retrieval model achieves 10.4% recall@1 (out of 1000 candidates) and the best photo intent prediction model achieves 58.1% F1 score, indicating that the dataset presents interesting yet challenging real-world problems. We are releasing PhotoChat to facilitate future research work among the community.