An investigation is made, via computer simulation, of the fate of radon gas produced in the lunar regolith by decay of uranium and thorium. The model used is that of radon atoms released and allowed to perform random walks within the lunar soil. Pressures based on results from Apollo lunar experiment packages indicate that the mean free path for such random walks will be the mean dimensions of void spaces within the soil rather than the (much longer) mean free path for collision with other gas molecules. Calculations are made, using various assumptions for mean void size, heat of adsorption of lunar material for radon, subsurface temperature profile, and depth of release, for the probability that a radon atom may escape through the regolith upper surface before it decays, to become part of the lunar "exosphere". Discussion is made of the implications such escape may have for lunar surface radioactivity and for lead/uranium dating of soil samples.