Ab initio total energy calculations within the Density Functional Theory framework were carried out for Pt(111), Pt(111)-p(2x2)-CO, Pt(111)-p(2x2)-O, and Pt(111)-p(2x2)-(CO+O) to provide an insight into the interaction between CO and O on metal surfaces, an important issue in CO oxidation, and also in promotion and poisoning effects of catalysis. The geometrical structures of these systems were optimized with respect to the total energy, the results of which agree with existing experimental values very well. It is found that (i) the local structures of Pt(111)-p(2x2)-(CO+O), such as the bond lengths of C-O, C-Pt, and O-Pt (chemisorbed O atom with Pt), are almost the same as that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively, (ii) the total valence charge density distributions in Pt(111)-p(2x2)-(CO+O) are very similar to that in Pt(111)-p(2x2)-CO, except in the region of the chemisorbed oxygen atom, and also nearly identical to that in Pt(111)-p(2x2)-O, apart from in the region of the chemisorbed CO, and (iii) the chemisorption energy of CO on a precovered Pt(111)-p(2x2)-O and the chemisorption energy of O on a precovered Pt(111)-p(2x2)CO are almost equal to that in Pt(111)-p(2x2)-CO and Pt(111)-p(2x2)-O, respectively. These results indicate that the interaction between CO and chemisorbed oxygen on a metal surface is mainly shore range in nature. The discussions of Pt-CO and Pt-O bonding and the interaction between CO and the chemisorbed oxygen atom on Pt(111) are augmented by local densities of states and real space distributions of quantum states.