Answering questions related to art pieces (paintings) is a difficult task, as it implies the understanding of not only the visual information that is shown in the picture, but also the contextual knowledge that is acquired through the study of the history of art. In this work, we introduce our first attempt towards building a new dataset, coined AQUA (Art QUestion Answering). The question-answer (QA) pairs are automatically generated using state-of-the-art question generation methods based on paintings and comments provided in an existing art understanding dataset. The QA pairs are cleansed by crowdsourcing workers with respect to their grammatical correctness, answerability, and answers' correctness. Our dataset inherently consists of visual (painting-based) and knowledge (comment-based) questions. We also present a two-branch model as baseline, where the visual and knowledge questions are handled independently. We extensively compare our baseline model against the state-of-the-art models for question answering, and we provide a comprehensive study about the challenges and potential future directions for visual question answering on art.