  The placement of a magnetic monopole into an electrically-neutral chiral
plasma with a non-zero axial density results in an electric polarization of the
matter. The electric current produced by the chiral magnetic effect is balanced
by charge diffusion and Ohmic dissipation, which generates a non-trivial charge
distribution. In turn, the latter induces a separation of chiralities along the
magnetic field of the monopole due to the chiral separation effect. We find the
stationary states of such a system, with vanishing total electric current and
stationary axial current balanced by the chiral anomaly. In this solution, the
monopole becomes "dressed" with an electric charge that is proportional to the
averaged chiral density of the matter -- forming a chiral dyon. The interplay
between the chiral effects on the one hand, and presence of magnetic field of
the monopole on the other, may affect the evolution of the monopole density in
the early Universe, contribute to the process of baryogenesis, and can also be
instrumental for detection of relic monopoles using chiral materials.
