Lateral potential energy curves for the chemisorption of CO on Pt{110} (1x1) and (1x2) along different azimuthal directions have been calculated using density functional theory slab calculations. In contrast to the simple models almost universally used, the results along <<1(1)over bar>0 > show that there is a barrier of similar to 0.15 eV between bridge and atop sites. Both bridge and atop sites are local minima. Diffusion along < 100 > on the (1x1) surface is strongly inhibited by a barrier greater than or equal to 1.2 eV. Quasielastic helium atom scattering data require reanalysis in the light of these results. The free energy, determining the most stable site at finite temperatures, includes a significant vibrational entropy term in the atop site.