We report a new morphology in a poly(isoprene-block-styrene-block-dimethylsiloxane ABC triblock copolymer. The most probable symmetry of the morphology (Ia3d) was determined from two-dimensional SAXS measurements performed on a sample with long-range order induced by an oscillatory shear field. By comparing the predictions of self-consistent field theory with TEM and SAXS and SANS powder diffraction patterns, we deduced that the morphology is a core-shell gyroid comprised of two independent and triply periodic poly(dimethylsiloxane) networks encased in poly(styrene) shells and separated by a continuous poly(isoprene) domain. Thus, this unique nanostructure divides space into five independent, three-dimensionally continuous domains.