The deficiencies of the local density approximation (LDA) to describe weakly adsorbed species on ionic surfaces are exposed in the current study of CO on the (001) surface of MgO. We applied a periodic formulation of density functional theory with crystal orbitals and charge density expanded as linear combinations of atomic orbitals of Gaussian form. The binding was investigated for four orientations of the CO molecule: either the carbon or oxygen atom of CO down over either the surface magnesium cation or oxygen anion. We find that the carbon down over the magnesium cation is the only noticeably attractive configuration, when basis set superposition error is corrected for, and we estimate the binding energy of CO to be 1.9 kcal/mol for the Perdew, Burke, and Enzerhof (PBE96) functional. The binding energy obtained in the LDA approximation is as large as 7.4 kcal/mol. For the C-down-over-Mg configuration, the CO stretching frequency shift is only 4 cm(-1) for the PBE96 functional. This binding energy, vibrational shift, and our analysis of density of states indicate that little chemical bonding accompanies the adsorption. The values of our binding energy and vibrational shift support a suggestion by Nygren and Pettersson [J. Chem. Phys, 1996, 105, 9339] that the CO adsorption discussed by He et al. [Surf. Sci. 1992, 261, 164] actually takes place at defect sites on the (001) surface of MgO.