Epitaxy of ZnO layers on cubic GaP (111) substrates has been demonstrated using pulsed laser deposition. Out of plane and in-plane epitaxial relationship of ZnO layer with respect to GaP substrate determined using phi scans in high resolution X-ray diffraction measurements are (0001) ZnO || (111) GaP and (-1 2 -1 0) ZnO || (-1 1 0) GaP respectively. Our results of epitaxy of ZnO and its intense excitonic photoluminescence with very weak defect luminescence suggest that (111) oriented GaP can be a potential buffer layer choice for the integration of ZnO based optoelectronic devices on Si(111) substrates.