We compute quasinormal modes (QNMs) of the metric and gauge field perturbations about black branes electrically and magnetically charged in the Einstein-Maxwell-Chern-Simons theory. By the gauge/gravity correspondence, this theory is dual to a particular class of field theories with a chiral anomaly, in a thermal charged plasma state subjected to a constant external magnetic field, B. The QNMs are dual to the poles of the two-point functions of the energy-momentum and axial current operators, and they encode information about the dissipation and transport of charges in the plasma. Complementary to the gravity calculation, we work out the hydrodynamic description of the dual field theory in the presence of a chiral anomaly, and a constant external B. We find good agreement with the weak field hydrodynamics, which can extend beyond the weak B regime into intermediate regimes. Furthermore, we provide results that can be tested against thermodynamics and hydrodynamics in the strong B regime. We find QNMs exhibiting Landau level behavior, which become long-lived at large B if the anomaly coefficient exceeds a critical magnitude. Chiral transport is analyzed beyond the hydrodynamic approximation for the five (formerly) hydrodynamic modes, including a chiral magnetic wave.