The optical and mechanical design and performance of the Submillimeter High Angular Resolution Camera (SHARC) is described. The camera currently operates with a monolithic 24-pixel linear bolometer array in the 350 and 450 juum atmospheric windows at the Caltech Submillimeter Observatory (CSO). The design extends the techniques of geometric optics employed in optical and near-infrared cameras to submillimeter wavelengths. Using an off-axis ellipsoidal mirror and cold stops, excellent imaging (Strehl ratio >0.95) is achieved across a 2' by 2' focal plane field even with secondary throws of up to 4'. The camera's symmetric mechanical assembly provides fixed, machined alignment of the optical elements. We demonstrate the imaging capabilities of the system with 350 /xm observations of a point source at the telescope. The optical design can easily accommodate future planned upgrades to two-dimensional bolometer arrays.