A microphase-separated poly(styrene-b-(lauryl-co-stearyl acrylate)-b-styrene) (SAS) triblock copolymer exhibiting a disordered spherical microstructure with randomly oriented grains was aligned through the application of large-amplitude oscillatory shear (LAOS) at a temperature below the order disorder transition temperature of the triblock copolymer, yet above the glass transition temperature of the polystyrene spherical domains. The thermoplastic elastomeric behavior of the SAS triblock copolymer provided a convenient means to observe the aligned morphology. Following application of LAOS, the specimen was quenched to room temperature (below the glass transition temperature of polystyrene), and small-angle X-ray scattering data were obtained in the three principal shear directions: shear gradient, velocity, and vorticity directions. The analysis revealed that the SAS triblock copolymer formed coexisting face-centered cubic and hexagonally dose-packed spherical microstructures. The presence of a dose-packed microstructure is in stark contrast to an extensive body of literature on sphere-forming bulk block copolymers that favor body-centered cubic systems under quiescent conditions and under shear. The aligned microstructure observed in this bulk block copolymer was reminiscent of that observed in various spherical soft material systems such as colloidal spheres, sphere-forming block copolymer solutions, and star polymer solutions. The highly unanticipated observation of dose-packed spherical microstructures in a neat block copolymer under shear is hypothesized to originate from the dispersity of the block copolymer.