We propose a new class of "grand challenge" AI problems that we call creative captioning---generating clever, interesting, or abstract captions for images, as well as understanding such captions. Creative captioning draws on core AI research areas of vision, natural language processing, narrative reasoning, and social reasoning, and across all these areas, it requires sophisticated uses of common sense and cultural knowledge. In this paper, we analyze several specific research problems that fall under creative captioning, using the popular board game Dixit as both inspiration and proposed testing ground. We expect that Dixit could serve as an engaging and motivating benchmark for creative captioning across numerous AI research communities for the coming 1-2 decades.