Research into organizations has concluded that organizational effectiveness is paradoxical, i.e., effective organizations have attributes that are simultaneously contradictory, even mutually exclusive. Although projects are temporary organizations, the paradox lens has largely been omitted in their context. This paper is an attempt to rectify the situation. It introduces a framework of eleven paradoxical tensions, concerning priority, structure, and execution of projects, wishing that it would encourage future research on paradoxical tensions of project management.