Using scanning tunneling microscopy and spectroscopy, we probe the electronic structures of single layer MoS2 on graphite. The apparent quasiparticle energy gap of single layer MoS2 is measured to be 2.15 ± 0.06 eV at 77 K, albeit a higher second conduction band threshold at 0.2 eV above the apparent conduction band minimum is also observed. Combining it with photoluminescence studies, we deduce an exciton binding energy of 0.22 ± 0.1 eV (or 0.42 eV if the second threshold is use), a value that is lower than current theoretical predictions. Consistent with theoretical predictions, we directly observe metallic edge states of single layer MoS2. In the bulk region of MoS2, the Fermi level is located at 1.8 eV above the valence band maximum, possibly due to the formation of a graphite/MoS2 heterojunction. At the edge, however, we observe an upward band bending of 0.6 eV within a short depletion length of about 5 nm, analogous to the phenomena of Fermi level pinning of a 3D semiconductor by metallic surface states.