This paper presents the Interactive Storyteller, a multi-user interface for AI-based interactive storytelling, where stories emerge from the interaction of human players with intelligent characters in a simulated story world. To support face-to-face contact and social interaction, we position users around a shared multi-touch table, which very much resembles the social setting of traditional tabletop board games. To our knowledge, the Interactive Storyteller is the first AI-based interactive storytelling system that combines an emergent narrative approach with the social aspects of traditional tabletop board games. We carried out user experiments to investigate to what extent our system supports social interaction. By analysing the interactions of pairs of children with the Interactive Storyteller, we determined which system aspects triggered cooperation and highly social behaviour and which aspects caused players to behave less socially. We also tried to find out whether the use of tangible playing pieces offered any advantages over touch-only interaction, but we did not find any differences between the two.