A nonequilibrium solid solution of 2% CH4 in Ne has been prepared by the matrix isolation technique. The system retains the fcc structure of pure Ne. A broad distribution of methane tunneling frequencies centered at an energy transfer of 0.5 meV is observed by inelastic neutron scattering. All CH4 molecules contribute to this distribution. For geometric reasons, to be consistent with the long range order of the matrix, the guest molecules must appear as trimers or higher multimers. The variety of aggregates with differing local surroundings and the complex level schemes of clusters of interacting molecules produce the broad distribution of tunnel transitions. Annealing leads to a wider potential distribution. In thermal equilibrium methane is insoluble in neon.