  We analyze the Chiral Magnetic Effect for non-Hermitian fermionic systems
using the biorthogonal formulation of quantum mechanics. In contrast to the
Hermitian chiral counterparts, we show that the Chiral Magnetic Effect may take
place in thermal equilibrium of an open non-Hermitian system with, generally,
massive fermions. The key observation is that for non-Hermitian charged
systems, there is no strict charge conservation as understood in the Hermitian
case, so the Bloch theorem preventing currents in the thermodynamic limit in
equilibrium does not apply.
