The diffusion of hydrogen atoms on a reconstructed Si(111)-(7X7) surface has been investigated using variational phase-space theory methods. The dimer-adatom-stacking (DAS) fault model of the reconstructed Si(111)-(7X7) surface proposed by Takayanagi et al. is employed to describe a four-layer lattice structure containing 292 atoms. The lattice potential is that developed by Bolding and Andersen; the gas-lattice interaction potential is described by a sum of Morse functions and bending terms between the hydrogen adatom and the Si atoms in the first and second layers. Canonical Markov walks with importance sampling are used to evaluate the flux across a set of dividing surfaces separating different adsorption sites. The minimum jump frequencies are then used as input to a set of coupled phenomenological kinetics equations that describe the diffusion rates of adatoms between adjacent adsorption sites. The diffusion coefficients D at different temperatures are computed from the slope of plots of the time variation of the root-mean-square displacements obtained from the solution of the rate equations. The results at 300, 500, and 800 K yield D=0.023 exp(- 1.54 eV/kT) cm(2)/s. The calculated activation energy of 1.54 eV is in excellent agreement with the experimental results obtained by Reider er al. using an optical second-harmonic diffraction technique. The coordinates corresponding to the minimum energy diffusion path suggest that hydrogen-atom diffusion between atop sites occurs along paths that involve lattice penetration. Calculated upper limits for the tunneling rates at 300, 500, and 800 K show that tunneling processes make only a small contribution to the total diffusion rate.