Beams of atomic hydrogen are known to react with halogens adsorbed on metal surfaces, and an Eley-Rideal mechanism has been suggested. The collinear reaction of gas phase H with Cl atoms adsorbed on an Au(111) surface is explored-using time dependent quantum techniques. Probabilities for reaction and reflection are computed as a function of incident ii energy and Cl-metal vibrational state. The time evolution is examined and a long lived intermediate is found to exist in which the Cl is bound to both the H and the metal. The probability for Eley-Rideal reaction is found to be small, on the order of a few to several percent, due primarily to the mass mismatch. The vibrational distribution of the product HCl and the temperature dependence of the reaction probability are in agreement with experiment.