  We derive a chiral kinetic theory with Landau level basis, which is valid for
slow-varying magnetic field with arbitrary magnitude. We apply the new chiral
kinetic theory to calculate the electric conductivity transverse to the
magnetic field in a magnetized QED and QCD plasma. Under the lowest Landau
level approximation and relaxation time approximation, we find the transverse
conductivity approaches a constant in the large magnetic field limit and is
inversely proportional to the relaxation time. We also obtain a
frequency-dependent transverse conductivity in response to a time-dependent
electric field. We find a high frequency enhancement in this conductivity.
