The kinetics of the oxidation of carbon monoxide on Pt(111) surfaces was studied isothermally by using an effusive directional molecular beam in an arrangement based on a variation of the dynamic method originally devised by King and Wells. Three temperature regimes were identified for this reaction on surfaces precovered with atomic oxygen. Below 300 K no reaction is observed, and the presence of preadsorbed atomic oxygen on the surface does not significantly affect the initial sticking coefficient of CO but only reduces its saturation coverage by less than half, which it does by preferentially blocking the bridge sites. Above 400 K, on the other hand, the desorption of CO2 from oxygen-covered surfaces is controlled by the impinging frequency of the incoming CO. The most interesting temperature range is that between 300 and 400 K, where the rate of surface recombination of CO with oxygen competes with that of CO adsorption; under those conditions the overall dynamic behavior is fairly complex, and not all the surface oxygen is reactive. Furthermore, the reaction rates in this regime not only depend on the coverages of the reactants, but also on how the surface is prepared. Two kinetically distinct types of oxygen atoms develop during the course of reaction in spite of the fact that they all sit on identical sites at the start of the kinetic runs, suggesting that the reactivity of chemisorbed CO depends on the local oxygen coverage of neighboring sites. We propose that such local arrangements modify the adsorption energy for atomic oxygen, and that this in turn changes the activation energy for the oxidation reaction. Previous reported molecular beam experiments were also extended to cover a wider range of surface coverages in order to better determine the dependence of the rate constant for the surface oxidation step on the coverages of CO and oxygen. It was found that while the presence of oxygen on the surface helps the production of CO2, increasing CO coverages augment the activation barrier for this reaction, an observation that is in direct contrast with previous reports. Finally, the adsorption sites for CO during the surface CO+O recombinatory reaction were characterized by reflection-absorption infrared spectroscopy. The data reported here is analyzed and discussed in terms of possible kinetic models.