A model of time-consistent procrastination is developed to assess the extent to which the observed behavior is compatible with rational behavior. When a finite work requirement must be completed by a deadline, the remaining time for leisure is an exhaustible resource. With a positive rate of time preference, the optimal allocation of this resource results in more hours spent working (and fewer in leisure) the closer the deadline. Key qualitative findings of psychological studies of academic procrastination are consistent with the standard natural resource management principles implied by the model, when suitably adapted to task aversiveness, uncertainty, and multiple deadlines. However, quantitatively, the fully rational model requires an extremely high rate of time preference or elasticity of intertemporal substitution to generate serious procrastination; furthermore, it cannot explain undesired procrastination. A companion paper, "Read This Paper Even Later: Procrastination with Time Inconsistent Preferences" analyzes the extent to which alternative time discounting preferences can better explain such impatience and address the issue of self-control failures.