Knowledge of the kinetics of oxide formation on an ultrathin copper (Cu) film is important both for fundamental understanding and for application, such as the use of copper as interconnects in semiconductor integrated circuits. We used angle resolved X-ray photoelectron spectroscopy to study the growth mechanism of Cu oxides at ambient conditions over times ranging from 1h to 120 days after the preparation of a 50nm-thick epitaxial Cu(100) film. We analyzed high resolution spectra near O 1s, Cu 2p and Cu LMM peaks to understand the kinetics of oxidation and to estimate overall oxide thickness as a function of time. We demonstrate that the oxide thickness of the epitaxial Cu film follows approximately an inverse logarithmic growth rate law, and that the rate of oxidation is substantially slower in epitaxial films than in polycrystalline films reported in the literature.