A cubic variant of CaH2 adopting a fluorite type crystal structure was synthesized by cationic substitution with La or Y, yielding the first alkaline earth hydride-based with fluorite-type framework. The material has a bandgap of similar to 2.5 eV (greenish yellow in color), which is much smaller than that of orthorhombic PbCl2-type CaH2 (4.4 eV) and is, in fact, the smallest among alkaline or alkaline earth metal hydrides reported to date. Analysis of the density functional theory band structure of cubic-CaH2 indicates that its conduction band minimum is formed mainly by the interaction between the Ca 3d e(g) orbitals around the crystallographic cavity defined by cubes of H- ions. The use of such cavities in the creation of lowlying conduction band minima by semiconductors is extremely rare, and has similarities to inorganic electrides.