A growing body of work in games research, both generative and analytic, seeks to characterize the relationship between a player’s understanding of an interactive narrative and her options for action within it. This paper provides several definitions that collectively serve as a basis for a model of the user’s comprehension of an unfolding story in a game. Central to this approach, we define the notion of narrative affordance. In essence, a game provides a narrative affordance for some course of action when a player can imagine that course of action as part of a story that completes their current story experience. To define narrative affordance, we draw links from cognitive models of narrative comprehension and a range of research on affordance, which we couple with planning approaches to story and discourse generation. In our approach, we view the creation of an interactive narrative that provides a high degree of agency as a discourse generation problem. We posit that an interactive narrative system must reason about the content and organization of its communication with a player in order to prompt a player’s understanding about the game’s story and her role in it. This paper ends by pointing toward a research direction intended to provide insight into a range of aspects of interactive narrative, including role, genre, choice and agency.