Controlled/"living" polymerizations and tandem polymerization methodologies offer enticing opportunities to enchain a wide variety of monomers into new, functional block copolymer materials with unusual physical properties. However, the use of these synthetic methods often introduces nontrivial molecular weight polydispersities, a type of chain length heterogeneity, into one or more of the copolymer blocks. While the self-assembly behavior of monodisperse AB diblock and ABA triblock copolymers is both experimentally and theoretically well understood, the effects of broadening the copolymer molecular weight distribution on block copolymer phase behavior are less well-explored. We report the melt-phase self-assembly behavior of SBS triblock copolymers (S = poly(styrene) and B = poly(1,4-butadiene)) comprised of a broad polydispersity B block (M-w/M-n = 1.73-2.00) flanked by relatively narrow dispersity S blocks (M-w/M-n = 1.09-1.36), in order to identify the effects of chain length heterogeneity on block copolymer self-assembly. Based on synchrotron small-angle X-ray scattering and transmission electron microscopy analyses of seventeen SBS triblock copolymers with poly(1,4-butadiene) volume fractions 0.27 <= f(B) <= 0.82, we demonstrate that polydisperse SBS, triblock copolymers self-assemble into periodic structures with unexpectedly enhanced stabilities that greatly exceed those of equivalent monodisperse copolymers. The unprecedented stabilities of these polydisperse microphase separated melts are discussed in the context of a complete morphology diagram for this system, which demonstrates that narrow dispersity copolymers are not required for periodic nanoscale assembly.