  We study the electrodynamics of a chiral medium with electric and magnetic
charges using the effective Maxwell-Chern-Simons theory extended to include the
magnetic current. The exchange of helicity between the chiral medium and the
magnetic field, known as the inverse cascade, is controlled by the chiral
anomaly equation. In the presence of the magnetic current, the magnetic
helicity is dissipated, so that the inverse cascade stops when the magnetic
helicity vanishes while the chiral conductivity reaches a non-vanishing
stationary value satisfying $\sigma_\chi^2< 4\sigma_e\sigma_m$, where
$\sigma_e$, $\sigma_m$ and $\sigma_\chi$ are the electric, magnetic and chiral
conductivities respectively. We argue that this state is superconducting and
exhibits the Meissner effect for both electric and magnetic fields. Moreover,
this state is stable with respect to small magnetic helicity fluctuations; the
magnetic helicity becomes unstable only when the inequality mentioned above is
violated.
