The Jupiter Icy Moons Orbiter (JIMO) is proposed by NASA as the next step in the exploration of the Jovian system following the successful Galileo project. JIMO would use nuclear-electric propulsion to deliver a highly capable scientific payload to Jupiter and go into orbit around Europa, Ganymede, and Callisto, and to conduct investigations of the Jovian system. In early 2003, a NASA Science Definition Team (SDT) was appointed to develop the scientific rationale and priorities for JIMO. The SDT, co-chaired by T. Johnson and R. Greeley, consisted of 38 scientists representing the broad scientific potential afforded by JIMO. This article summarizes the principal findings of the SDT. The scientific foundations for the proposed JIMO mission include recommendations from previous studies by the National Research Council, which identify Europa and the Jupiter system as high-priority objects for solar system exploration and the search for life's origin. In addition to these documents, input to the SDT was obtained from a community-wide meeting titled Forum on concepts and approaches for the Jupiter Icy Moons Orbiter.