Heterostructures involving ZnS/GaN show promise for the injection of holes from p-GaN into n-ZnS. This combination could result in multi-color electroluminescent displays. We have grown single crystal ZnS on GaN and sapphire (0001) by MBE using elemental sources. The ZnS was grown at temperatures from 150°C–400°C, with beam flux equivalent pressures of (0.3 – 2.0) × 10−7 torr. Growth rates of up to 0.4 μm per hour were observed for the lower growth temperatures, with rapidly diminishing rates for temperatures above 350μC. The GaN substrate consisted of a 3 μm epilayer grown on sapphire by MOCVD. XPS analysis revealed the presence of carbon surface contamination on the GaN, which was removed by in situ exposure to an RF nitrogen plasma. RHEED observations indicate that the zincblende ZnS layers commonly contain (111) twins, although twin free films may be grown at a high substrate temperature. The samples were characterized using photoluminescence and X-ray diffraction. X-ray peaks typically had FWHM of 400 arcsec for ω/2θ scans, and somewhat worse for ω scans. Photoluminescence spectra of the ZnS films doped with Ag and Al demonstrated the well known blue donor acceptor transition at 440 nm.