We report the first observation of atomic long range ordering in the metal-oxide based wide bandgap (3.68 eV) ZnMgO alloy semiconductor thin films grown on sapphire (0001) by pulsed laser deposition. The ZnMgO system has the hexagonal wurtzite structure. The atomic ordering was deduced from the observations of forbidden x-ray diffraction peaks in the wurtzite structure. We show that under optimum thin film growth conditions, Zn and Mg preferentially occupy hcp sublattice. The relative intensity of the superlattice peak was largest for the Mg content in the range of 10%, which is about 50% of the solubility of Mg in ZnO. The observation of long range order in ZnMgO alloy semiconductor is quite important in the context of understanding issues related to the growth kinetics, surface reconstruction, and phase stability of metal-oxide based heterostructures and devices.