Confined ionic liquids in hydrophilic porous media have disrupted lattices and can be divided into two layers: An immobile ion layer adheres to the pore surfaces, and an inner layer exhibits faster mobility than the bulk. In this work, we report the first study of ionic liquids confined in block copolymer-based porous carbon fibers (PCFs) synthesized from polyacrylonitrile-block-polymethyl methacrylate (PAN-b-PMMA). The PCFs contain a network of unimodal mesopores of 13.6 nm in diameter and contain more hydrophilic surface functional groups than previously studied porous carbon. Elastic neutron scattering shows no freezing point for 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM]BF4) confined in PCFs down to 20 K. Quasi-elastic neutron scattering (QENS) is used to measure the diffusion of [BMIM]BF4 confined in PCFs, which, surprisingly, is 7-fold faster than in the bulk. The unprecedentedly high ion diffusion remarks that PCFs hold exceptional potential for use in electrochemical catalysis, energy conversion, and storage.