Characteristics of a new ring Compton scatter camera are described. This camera is designed to image medium energy (0.5 to 3 MeV) gamma-ray fields. It consists of two position sensitive detector arrays: a 4x4 planar array of high purity germanium (HPGe) crystals and a ring array of up to 64 NaI(Tl) crystals. Past evaluations of Compton cameras have employed a planar second detector, which is subjected to a Large flux of gamma rays that either pass directly through or undergo small angle scatter in the first detector. A ring array significantly reduces direct and small angle scattered events in the second detector. An analytical model for ring camera systems has been developed to predict angular resolution and efficiency, and has been benchmarked against measurements made with a prototype system consisting of the 4x4 HPGe array and an 8 element ring. Predictions are made for a system with 64 crystals in the second detector ring.