Motivated by applications to the quark gluon plasma state generated in heavy ion collisions, I study a 4-dimensional supersymmetric conformal field theory in the thermal state, carrying axial charge, and subject to a strong external magnetic field, B. This theory has a chiral anomaly, which conspires with the magnetic field and axial charges to give rise to a host of novel transport phenomena. According to the gauge/gravity correspondence, also referred to as holography the described field theory state is dual to a charged magnetic black brane which is a solution of Einstein-Maxwell-Chern-Simons theory. I compute the quasinormal modes which are holographically dual to the poles of the two-point functions of the energy-momentum tensor and axial current operators, encoding information about the dissipation and transport of charges in the plasma. I derive general results in the hydrodynamic field theory and confirm them by explicit solutions in the dual gravity theory. Chiral transport is analyzed beyond the hydrodynamic approximation for the five hydrodynamic modes, one of which turns from a purely dissipative diffusion mode into a propagating chiral magnetic wave mode. I derive Kubo formulas for the thermodynamic and hydrodynamic transport coefficients in this plasma state. I analyze the discrete symmetries and Onsager relations of the corresponding correlators. I provide the transport coefficients in the holographic theory including both DC values and their frequency, ω, dependence. The chiral magnetic conductivity and magneto-vortical susceptibilities are independent of B for all ω while the chiral vortical conductivity and chiral heat conductivity have dependence when B≠ω. The parallel and perpendicular shear viscosity are found to be cubic in ω, while conductivity is linear in ω in the conformal limit ω≫T. AC values of Hall conductivity are found to dominate by n0/B term when ω≫T, while that of Hall viscosity quickly decays to zero near ω∼T.