We present first principles calculations of the potential energy surface for the diffusion of a single hydrogen atom on Si(100)2×1. Surface relaxation is found to be very important for the energetics of diffusion. A strong anisotropy is predicted for hydrogen motion: H should diffuse mainly along dimer rows, where activation energies are ∼ 1.3 eV, while the barrier for row-to-row hopping is ∼ 0.5 eV higher. Our results indicate that diffusion can be considered a fast process compared to H₂ recombinative desorption.