Periodic Hartree-Fock total energy calculations on two-dimensionally periodic slabs have been used to predict the equilibrium geometry of a monolayer of carbon monoxide molecules adsorbed on the nonpolar (<10(1)over bar 0>) surface of ZnO. Two physisorbed (or weakly chemisorbed) minimum energy configurations are found. In one the CO molecules adsorb with their oxygen atoms coordinated to surface Zn atoms, while in the other the carbon atoms are coordinated to surface Zn atoms. The two calculated minima are very close in energy. In the second geometry, the C-Zn "bond" and the C-O bond make angles of 32.5 degrees and 39.5 degrees with the surface normal, and the intramolecular bond shortens slightly from its free value in reasonable agreement with experimental results. No binding of CO to the surface oxygen atoms is predicted. Surface-related changes in the vibrational frequencies for the adsorbed molecules agree reasonably well with infrared spectroscopic data, and the "carbon-down" binding energy of the molecule with the surface is in good agreement with thermal desorption data (though electron correlation effects have to be included in the calculation to obtain acceptable results for low surface coverage).