We report a new generation of nanodielectric energy storage materials based on supramolecular block copolymers. In our approach, highly polarizable, conducting nanodomains are embedded within an insulating matrix through block copolymer microphase separation. An applied electric field leads to electronic polarization of the conducting domains. The high interfacial area of microphase-separated domains amplifies the polarization, leading to high dielectric permittivity. Specifically, reversible addition fragmentation transfer (RAFT) polymerization was used to prepare block copolymers with poly(methyl acrylate) (PMA) as the insulating segment and a strongly acidic dopant moiety, poly-(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPSA), as the basis for the conducting segment. The PAMPSA block was complexed with an oligoaniline trimer to form a dopant-conjugated moiety complex that is electronically conductive after oxidation. For the undoped neat block copolymers, the increase of the PMA block length leads to a transition in dielectric properties from ionic conductor to dielectric capacitor with polarization resulting from migration of protons within the isolated PAMPSA domains. The oligoaniline-doped copolymers show remarkably different dielectric properties. At frequencies above 200 kHz, they exhibit characteristics of dielectric capacitors with much higher permittivity and lower dielectric loss than the corresponding undoped copolymers.