The influence of CO adsorption on the Shockley type surface state on vicinal Cu(111) surfaces is investigated using angle resolved photoemission. As the steps are decorated with CO the surface state shifts to higher binding energies, which is opposite to the known behavior on flat Cu(111). This is described within a one-dimensional potential model in which clean steps represent repulsive barriers and decorated steps become attractive wells. From the coverage dependence the integrated CO well potential can be quantified. It is U(CO)a = -2.9 eV A on both Cu(332) and Cu(221) surfaces. Density functional calculations reveal that this attractive potential is due to the very local charge transfer from the Cu step atom to the adsorbed molecule.