We report the near-edge x-ray absorption fine-structure (NEXAFS) spectrum of a single layer of graphite (graphene) obtained by micromechanical cleavage of highly ordered pyrolytic graphite on a SiO2 substrate. We utilized a photoemission electron microscope to separately study single-, double-, and few-layers graphene samples. In single- layer graphene we observe a splitting of the pi* resonance and a clear signature of the predicted interlayer state. The NEXAFS data illustrate the rapid evolution of the electronic structure with the increased number of layers.