The associative desorption of hydrogen atoms on graphite via an Eley-Rideal mechanism is studied theoretically. Time-independent quantum reactive scattering calculations are performed on a potential energy surface calculated using the generalised gradient approximation of density functional theory. The absence of a barrier to reaction leads to a reaction probability which is close to one, even for low collision energies. The vibrational product distribution of H-2 shows a peak in the (upsilon = 2) vibrational state with appreciable population of higher states. The significance of these results for chemistry in the interstellar medium is discussed.