We have studied the growth of Cu deposited by molecular beam epitaxy at room temperature on the O-terminated ZnO (0001) surface. The structural properties of Cu on ZnO were investigated by X-ray scattering, atomic force microscopy (AFM) and scanning electron microscopy (SEM). Chemical characterisation was performed by X-ray photoemission spectroscopy (XPS). X-ray diffraction studies reveal a predominant (111) out-of plane texture and the [110] C u ||[1120] Z n O and [112] C u ||[1010] Z n O azimuthal orientation of the Cu. The XPS spectra show that the ZnO (0001) surface is completely covered after a Cu deposition with a nominal thickness of 50A. AFM and SEM images clearly indicate that at later deposition states Cu clusters increase laterally and later coalesce.