Self-assembled-monolayers (SAMs) of aromatic thiolates on metal surfaces are candidates for molecular "quantum dots" or "wires". We probe the interfacial electronic structure using two-photon photoemission in SAMs of pentafluorothiophenolate (C6F5S-) on Cu(111). Compared to gas-phase C6F5SH, the σ* LUMO in the assembled molecule is stabilized by 3.1 eV and the HOMO-LUMO gap is reduced by 5.7 eV. Ab initio calculations reveal that stabilization of molecular states is, to a great extent, a consequence of the strong electronic coupling between metal and molecular orbitals via the -S- bridge. This strong electronic coupling is absent when the molecule is not directly bonded to the surface, as in the case of C6F6 weakly adsorbed on Cu(111).