The self-assembly of diblock copolymers provides a convenient route to the formation of mechanically robust films with precise and tunable periodic arrangements of two physically demixed but chemically linked polymeric materials. Chemoselective transport membranes may be realized from such films by selective partitioning of an active species into one of the polymer domains. Here, lithium ions were selectively sequestered within the poly(ethylene oxide) block of a liquid crystalline diblock copolymer to form polymer electrolyte membranes. Optimization of the membrane conductivity mandates alignment of self-assembled structures such that conduction occurs via direct as opposed to tortuous transport between exterior surfaces. We show here that magnetic fields can be used in a very simple and scalable manner to produce highly aligned hexagonally packed cylindrical microdomains in such membranes over macroscopic areas. We systematically explore the dependence of the ionic conductivity of the membrane on both temperature and magnetic field strength. A surprising order of magnitude increase in conductivity relative to the nonaligned case is found in films aligned at the highest magnetic field strengths, 6 T. The conductivity of field aligned samples shows a nonmonotonic dependence on temperature, with a marked decrease on heating in the proximity of the order-disorder transition of the system before increasing again at elevated temperatures. The data suggest that domain-confined transport in hexagonally packed cylindrical systems differs markedly in anisotropy by comparison with lamellar systems.