A Conversion Electron Mössbauer Spectrometer to be used for the characterization of Fe-containing metal surfaces was designed and installed in an Ultra High Vacuum chamber. The design is based in the use of a Channeltron electron multiplier for the detection of electrons emerging from the sample after an incident γ-Ray is absorbed by resonant nuclear excitation. Using a Monte Carlo simulation for electron trajectories in solids the mean-escape-depth of the detected Mössbauer signal from a metallic iron sample was estimated to be 80 nm, assuming that the main signals being detected correspond to the Fe(M), Fe(L) and Fe(K) conversion electrons as well as the Fe(KLM), Fe(KLL) and Fe(LMM) Auger electrons. The sensitivity to the surface region was also estimated experimentally by acquiring Mössbauer spectra from a series of Fe films of different thickness deposited by magnetron sputtering on 304 stainless steel substrates.