  We demonstrate spatially resolved, coherent excitation of Rydberg atoms on an
atom chip. Electromagnetically induced transparency (EIT) is used to
investigate the properties of the Rydberg atoms near the gold coated chip
surface. We measure distance dependent shifts (~10 MHz) of the Rydberg energy
levels caused by a spatially inhomogeneous electric field. The measured field
strength and distance dependence is in agreement with a simple model for the
electric field produced by a localized patch of Rb adsorbates deposited on the
chip surface during experiments. The EIT resonances remain narrow (< 4 MHz) and
the observed widths are independent of atom-surface distance down to ~20 \mum,
indicating relatively long lifetime of the Rydberg states. Our results open the
way to studies of dipolar physics, collective excitations, quantum metrology
and quantum information processing involving interacting Rydberg excited atoms
on atom chips.
