The radiation emitted by electromagnetic sources placed both inside and outside of a homogeneous sphere of chiral media is studied using an exact formulation. For both cases, dyadic Green’s functions are found in terms of spherical vector wave functions. The radiated fields and radiation resistance are examined for a dipole located at the center of the chiral sphere. For this case, it is shown that by choosing the sphere’s size and material parameters properly, purely circular polarization can be achieved in the far field. It is also demonstrated that the radiation resistance of the dipole can be increased.