In this work, we investigate the use of a three-stage Compton camera to measure secondary prompt gamma rays emitted from patients treated with proton beam radiotherapy. The purpose of this study was (1) to develop an optimal three-stage Compton camera specifically designed to measure prompt gamma rays emitted from tissue and (2) to determine the feasibility of using this optimized Compton camera design to measure and image prompt gamma rays emitted during proton beam irradiation. The three-stage Compton camera was modeled in Geant4 as three high-purity germanium detector stages arranged in parallel-plane geometry. Initially, an isotropic gamma source ranging from 0 to 15 MeV was used to determine lateral width and thickness of the detector stages that provided the optimal detection efficiency. Then, the gamma source was replaced by a proton beam irradiating a tissue phantom to calculate the overall efficiency of the optimized camera for detecting emitted prompt gammas. The overall calculated efficiencies varied from ∼ 10(-6) to 10(-3) prompt gammas detected per proton incident on the tissue phantom for several variations of the optimal camera design studied. Based on the overall efficiency results, we believe it feasible that a three-stage Compton camera could detect a sufficient number of prompt gammas to allow measurement and imaging of prompt gamma emission during proton radiotherapy.