Storytelling has recently become a popular way to guide museum visitors, replacing traditional exhibit-centric descriptions by story-centric cohesive narrations with references to the exhibits and multimedia content. This work presents the fundamental elements of the CHESS project approach, the goal of which is to provide adaptive, personalized, interactive storytelling for museum visits. We shortly present the CHESS project and its background, we detail the proposed storytelling and user models, we describe the provided functionality and we outline the main tools and mechanisms employed. Finally, we present the preliminary results of a recent evaluation study that are informing several directions for future work.