Traveling reaction fronts in the oxidation of hydrogen on a Pt(111) surface were investigated by means of scanning tunneling microscopy (STM). The fronts were observed during dosing of the oxygen covered surface with hydrogen at temperatures below 170 K. The fronts represented 10 to 100 nm wide OH-covered regions, separating unreacted O atoms from the reaction product H2O. O atoms were transformed into H2O by the motion of the OH zone. Small scale STM data showed the processes within the fronts on the atomic scale. Experiments on larger scale revealed the velocity and the width of the fronts as a function of temperature. A simple reaction-diffusion model has been constructed, which contains two reaction steps and the surface diffusion of water molecules, and qualitatively reproduces the experimental observations. A lower bound for the front velocity was also derived analytically. For a quantitative comparison between experiment and theory the rate constants of the two reaction steps and the diffusion coefficient of H2O were determined by STM and low energy electron diffraction experiments. With these parameters, the front velocities predicted by the model are approximately one order of magnitude smaller than those determined by STM. The predicted front widths are, depending on the temperature, between two and three orders of magnitude larger than the experimental values. We conclude that these deviations result from the inability of the reaction-diffusion system to describe the complex chemical processes and structure changes within the fronts. The atomically resolved STM data indicate attractive interactions between the particles that in particular affect the diffusion of the H2O molecules.