We address, by means of ab-initio calculations, the origin of the correlation that has been observed experimentally between the chemisorption energy of CO on nanoscale Cu(001) supported films and quantum-size effects. The calculated chemisorption energy shows systematic oscillations, as a function of film thickness, with a periodicity corresponding to that of quantum-well states at the surface-Brillouin-zone center crossing the Fermi energy. We explain this trend based on the oscillations, with film thickness, of the decay length on the vacuum side of the quantum-well states at the Fermi energy. Contrary to previous suggestions, we find that the actual oscillations with film thickness of the density of states per atom of the film at the Fermi energy cannot account for the observed trend in the chemisorption energy. ; Comment: 18 pages, 7 figures. Accepted for publication in Phys. Rev. B