  Starting from the modified Maxwell equations in Carroll-Field-Jackiw
electrodynamics we study the electromagnetic radiation in a chiral medium
characterized by an axion coupling $\theta(x)=b_\mu x^\mu$, with $b_\mu=
(0,\mathbf{b})$, which gives rise to the magnetoelectric effect. Employing the
stationary phase approximation we construct the Green's matrix in the radiation
zone which allows the calculation of the corresponding electromagnetic
potentials and fields for arbitrary sources. We obtain a general expression for
the angular distribution of the radiated energy per unit frequency. As an
application we consider a charge moving at constant velocity parallel to
$\mathbf{b}$ in the medium and discuss the resulting Cherenkov radiation. We
recover the vacuum Cherenkov radiation. For the case of a material with
refraction index $n > 1$ we find that zero, one or two Cherenkov cones can
appear. The spectral distribution of the radiation together with the comparison
of the radiation output of each cone are presented, as well as some angular
plots showing the appearance of the cones.
