We derive the hydrodynamic transport coefficients governing a quantum field theory with a chiral anomaly in a charged thermal fluid state, subjected to a strong external magnetic field. As a proof of existence, within a holographic model,  we compute most of these transport coefficients. In our model fluid, charged magnetic black branes in Einstein-Maxwell-Chern-Simons theory, the accessible transport coefficients are nonzero, while they show non-trivial dependence on the magnetic field, anomaly coefficient, and/or charge of the plasma. Some novel transport effects arise from the presence of a chiral anomaly, charge, and/or a magnetic field.