Directly measuring the rate of a surface chemical reaction remains a challenging problem. For example, even after more than 30 years of study, there is still no agreement on the kinetic parameters for one of the simplest surface reactions: desorption of CO from Pt(111). We present a new experimental technique for determining rates of surface reactions, the velocity-selected residence time method, and demonstrate it for thermal desorption of CO from Pt(111). We use UV-UV double resonance spectroscopy to record surface residence times at selected final velocities of the desorbing CO subsequent to dosing with a pulsed molecular beam. Velocity selection differentiates trapping-desorption from direct scattering and removes influences on the temporal profile arising from the velocity distribution of the desorbing CO. The kinetic data thus obtained are of such high quality that bi-exponential desorption kinetics of CO from Pt(111) can be clearly seen. We assign the faster of the two rate processes to desorption from (111) terraces, and the slower rate process to sequential diffusion from steps to terraces followed by desorption. The influence of steps, whose density may vary from crystal to crystal, accounts for the diversity of previously reported (single exponential) kinetics results. Using transition-state theory, we derive the binding energy of CO to Pt(111) terraces, D0terr (Pt-CO) = 34 +/- 1 kcal/mol (1.47 +/- 0.04 eV) for the low coverage limit (<= 0.03 ML) where adsorbate-adsorbate interactions are negligible. This provides a useful benchmark for electronic structure theory of adsorbates on metal surfaces.