Abstract : The Pierre Auger Observatory is a``hybrid'' UHECR detector. The surface detector (SD) and air fluorescence detector (FD) of the observatory are designed for observation of cosmic ray showers in coincidence, with a 10% duty cycle. The resulting data are expected to be superior in quality to those of either the SD or FD operating individually. Hybrid operation, triggering, data acquisition, and event reconstruction were successfully demonstrated during the prototype phase of the project. This paper focuses on 75 hybrid events recorded during a four month period of running with the prototype detectors in late 2001 and early 2002. The geometric technique for reconstruction of the hybrid events is described and its advantages over the traditional FD-only method are demonstrated. A lateral distribution for the water Cherenkov signals, derived from these data, is presented.