The dissociation of CH4 on a Ni surface is examined quantum mechanically. The molecule is treated as a quasidiatomic R-H, where R=CH3, and vibrational, rotational, and translational motion normal to the surface are included. The metal surface is assumed to be flat and the potential energy surface is based on ab initio studies of dissociation over the Ni(111) atop site. Lattice motion is introduced via the surface mass model. Bessel-Legendre and fast Fourier transform pseudospectral techniques are used to evolve the wave function in time, and energy resolved reactive fluxes are extracted via a time-to-energy transform. Agreement with experiment is good, particularly with regard to the dependence of the dissociation probability on incident energy and surface temperature. The dynamics of the dissociation reaction for the various initial states of the molecule are examined.