  We analyze the combined effects of hydrodynamic fluctuations and chiral
magnetic effect (CME) for a chiral medium in the presence of a background
magnetic field. Based on the recently developed non-equilibrium effective field
theory, we show fluctuations give rise to a CME-related positive contribution
to magnetoresistance, while the early studies without accounting for the
fluctuations find a CME-related negative magnetoresistance. At zero axial
relaxation rate, the fluctuations contribute to the transverse conductivity in
addition to the longitudinal one.
