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We present Doppler broadened gamma spectra, obtained using the newly developed advanced positron beam at the University of Texas at Arlington, from a sample consisting of 6 to 8 layers of graphene (MLG) on polycrystalline Cu. The kinetic energy of the positron beam was varied form 2 eV to 20 keV allowing for a depth resolved measurement. The ratio curves formed by dividing the measured Doppler broadened gamma spectra obtained at low positron kinetic energies (~2eV) to the gamma spectra obtained at 20 keV were compared to ratio curves found by dividing the calculated spectra of bulk graphite to bulk Cu. The ratio curves obtained from the measured results show qualitative agreement with those obtained from the calculated spectra. In particular, both sets of curves indicate a much reduced intensity at high momentum. The agreement between the measured and calculated curves is consistent with the hypothesis that the 2eV spectra correspond to the Doppler broadened spectra from the thin overlayer of Graphene (which we anticipate should be similar to the spectra obtained from bulk graphite) and that the spectra taken at 20 keV corresponds to bulk Cu due to the fact that most of the positrons implanted at this energy annihilate in the Cu substrate. The results taken at 2 eV provide evidence that it is possible to obtain chemically sensitive information from the top atomic layers of surfaces (both internal and external) from an analysis of the high momentum tail of the Doppler broadened gamma spectra obtained from the annihilation of positrons at the surface.