MgZnO thin films were grown on c-sapphire and ZnO-coated c-sapphire substrates by pulsed laser deposition from a ZnMgO target with 4 at% Mg. The MgZnO grown on the ZnO underlayer showed significantly better crystal quality than that grown directly on sapphire. AFM studies revealed a significant deterioration in surface morphology for the MgZnO layers compared with the ZnO underlayer. Optical transmission studies indicated a MgZnO bandgap of 3.61eV (compared with 3.34eV for the ZnO), which corresponds to a Mg content of about 16.1 at%. The MgZnO/ZnO heterojunction showed an anomalously low resistivity, which was more than two orders of magnitude less than the MgZnO layer and an order of magnitude lower than that for the ZnO layer. It was suggested that this may be attributable to the presence of a 2D electron gas at the ZnMgO/ZnO heterointerface.