Oxidation can deteriorate the properties of copper that are critical for its use, particularly in the semiconductor industry and electro-optics applications(1-7). This has prompted numerous studies exploring copper oxidation and possible passivation strategies(8). In situ observations have, for example, shown that oxidation involves stepped surfaces: Cu2O growth occurs on flat surfaces as a result of Cu adatoms detaching from steps and diffusing across terraces(9-11). But even though this mechanism explains why single-crystalline copper is more resistant to oxidation than polycrystalline copper, the fact that flat copper surfaces can be free of oxidation has not been explored further. Here we report the fabrication of copper thin films that are semi-permanently oxidation resistant because they consist of flat surfaces with only occasional mono-atomic steps. First-principles calculations confirm that mono-atomic step edges are as impervious to oxygen as flat surfaces and that surface adsorption of O atoms is suppressed once an oxygen face-centred cubic (fcc) surface site coverage of 50% has been reached. These combined effects explain the exceptional oxidation resistance of ultraflat Cu surfaces.