The electronic structure of thin Ca/Sr alloy films epitaxially grown on the topological insulator Bi2Se3 is investigated by first-principles calculations. Despite a negligible spin-orbit coupling in Ca/Sr alloys and strict spin degeneracy in freestanding Ca/Sr films, the topological surface states on the pristine Bi2Se3 surface are spatially transferred, upon Ca/Sr overlayer growth, into the overlayer to form topological quantum well resonances characterized by a spin-polarized chiral Dirac cone. The physical origin of this effect and the implications regarding applications are discussed.