Cuprous halides, characterized by a direct wide band-gap and a good lattice matching with Si, is an intrinsic p-type I-VII compound semiconductor. It shows remarkable optoelectronic properties, including a large exciton binding energy at room temperature and a very small piezoelectric coefficient. The major obstacle to its application is the difficulty in growing a single-crystal epitaxial film of cuprous halides. We first demonstrate the single crystal epitaxy of high quality cuprous iodide (CuI) film grown on Si and sapphire substrates by molecular beam epitaxy. Enhanced photoluminescence on the order of magnitude larger than that of GaN and continuous-wave optically pumped lasing were found in MBE grown CuI film. The intrinsic p-type characteristics of CuI were confirmed using an n-AlGaN/p-CuI junction that emits blue light. The discovery will provide an alternative way towards highly efficient optoelectronic devices compatible with both Si and III-nitride technologies.