Pilot studies are often used to transition therapies developed using animal models to a clinical setting. Frequently, the focus of such trials is on estimating the safety in terms of the occurrence of certain adverse events. With relatively small sample sizes, the probability of observing even relatively common events is low; however, inference on the true underlying event rate is still necessary even when no events of interest are observed. The exact upper limit to the event rate is derived and illustrated graphically. In addition, the simple algebraic expression for the confidence bound is seen to be useful in the context of planning studies.