Storytelling is a new way to guide museum visitors, where the traditional set of exhibit-centric descriptions is replaced by story-centric cohesive narrations with carfully-designed references to the exhibits. Personalized storrytelling customizes the narrations according to different user characteristics, either statically or dynamically during the visit. In this paper, we describe the basic elements of an effort towards achieving personalized storytelling for museum visits in the context of the CHESS project. We outline the user and story models employed, we detail the main tools and mechanisms to bootstrap personalization for first-time visitors, and we describe the overall system architecture. The results of some very preliminary experiments with actulal visitors are encouraging and show several directions for future work.