The structure of the Si(111)-CaF2 interface has been determined with medium-energy ion scattering. Ca bonds to the Si substrate in a geometric arrangement virtually identical to CaSi2. Half of the F atoms at the interface are missing; there is no F-Si bonding and the interface is charge neutral. The structure we find has not been considered previously and provides a natural explanation for the results of published photoemission studies. © 1988 The American Physical Society.