We demonstrate a novel approach to in-situ monitoring of reaction kinetics on surfaces, using vibrational sum frequency generation (VSFG). In this approach, vibrational spectra of adsorbed molecules are recorded using broadband VSFG as a function of surface temperature. The use of broadband VSFG allows us to obtain spectra of the vibrational resonances over a wide frequency range without tuning the infrared frequency, with good frequency resolution, in small temperature steps. This temperature-programmed vibrational sum frequency generation (TP-VSFG) technique complements conventional temperature-programmed desorption/reaction (TPD/TPR) techniques in that it probes (changes in) the molecules remaining on the surface during the chemical transformation, rather than those ending up in the gas phase. The intensity variations and frequency shifts of the vibrational resonances of surface molecules as chemistry is occurring on the surface contain detailed information on that chemistry. The technique is demonstrated for the benchmark reaction of the catalytic oxidation of carbon monoxide on a Pt(111) surface. Through investigating the temperature-dependent CO stretching vibration, we find that the rate of the oxidation is determined by the oxygen coverage. The activation energy is found to be (0.56 +/- 0.05) eV and the preexponential factor is (2.0 +/- 0.2) x 10(7) monolayers.s(-1), both in excellent agreement with previous measurements.