Strains in CaF2 films, grown by molecular beam epitaxy at 700ºC on Si(lll) subsrates, have been measured by MeV 4He+ ion channeling. For CaF2 films thinner than 200nm, the strain parallel to the (111) plane is found to be tensile. No strain is observed for films thicker than 200nm. The observed tensile strain cannot be explained by a simple pseudomorphic growth model because the larger lattice constant of CaF2 relative to Si should result in a compressive misfit strain. The tensile strain is an indication of the relaxation of the compressive misfit strain at the growth temperature due to nucleation of interfacial defects. If these defects are not annealed out as the substrate temperature is lowered after growth, the tensile strain can result because of the larger thermal contraction of CaF2 compared to Si. The final film quality near the interface improves as the film thickness is increased. This indicates that reordering of interfacial disorder is caused by the strain energy accumulated during the cooling process.