  We study the evolution of magnetohydrodynamic turbulence taking into account
the chiral anomaly effect. This chiral magnetohydrodynamic description of the
plasma is expected to be relevant for temperatures comparable to the
electroweak scale, and therefore for the evolution of magnetic fields in the
early Universe and young neutron stars. We focus on the case of freely decaying
chiral magnetohydrodynamic turbulence and discuss the dissipation of ideal MHD
invariants. Using the variational approach we discuss the minimum energy
configurations of magnetic field and velocity. As in the case of the standard
magnetohydrodynamic turbulence, we find that the natural relaxation state is
given by a force-free field, $\nabla \times \mathbf{B} \propto \mathbf{B}$.
However, the precise form of this configuration is now determined by parameters
describing the chiral anomaly effect, leading to some important differences
when compared to the non-chiral turbulence. Using this result we argue that the
evolution of velocity and magnetic field will tend to effectively decouple
during the transition to this minimal energy state.
