We present calculations of the broadening and the shifts of the Rydberg electron levels of a Xenon atom near a metal surface. The Xenon atom is described using a pseudopotenial. The energies and widths of the Xenon states, computed from the Schrodinger equation using the complex scaling method, exhibit a complicated distance dependence. We show that some of the orbitals hybridize, when the atom approaches the surface. This effect even causes the widths of some states to decrease with decreasing atom-surface separation.