This study examines how top management teams (TMTs) embrace ambiguity in the pursuit of radical innovation. TMTs face the distinct mandate to toggle between short-term and long-term thinking. Given this challenge, existing research has focused on TMTs’ bounded rationality and the attendant need for systems and structures designed to reduce uncertainty and simplify choice. In contrast, we suggest that under certain conditions leaders can benefit from leveraging, rather than lessening, ambiguity. Drawing from qualitative data of five distinct TMTs collected over a seven-year period, we analyze the often-shrouded process by which senior leaders explore novel possibilities for radical innovation. Our findings reveal “play” in contradistinction to “reason” as a novel form of organizational intelligence that is uniquely suited to moments of extreme ambiguity. We introduce the concept of a “play state,” which we define as a property of teams whereby members feel encouraged to explore imagined futures without immediate pressures towards certainty, commitment, or constraint. Together, by highlighting the generative properties of ambiguity and play, this study seeks to complicate the primacy of rationality that often typifies theories of innovation decision-making. Keywords: innovation; top management teams; ambiguity; play, organizational intelligence