We have used a `hole-burning' technique to study the mobility of thin solid films of H2 and D2 for temperatures between 1.6 K and 5 K. Even at low temperatures where transport through the vapor is negligible, the solid films remain mobile. The transport is thermally activated with an activation energy of 19 K for H2 and 38 K for D2. The time dependence of the regrowth shows that surface transport is not due to simple diffusion.