In this paper, a formulation for the dyadic Green's function of cylindrical multilayered chiral media is presented at first using the methods of eigenfunction expansion and scattering superposition. The specific expressions of the dyadic Green's function are also found in terms of normalized cylindrical vector wave functions, when the electric current sources are placed both inside and outside of a chiral circular cylinder and a cylindrical chirodome. The radiation characteristics of a point dipole antenna on the axis of chiral circular cylinder and cylindrical chirodome are analysed. For both cases, the results show that by changing the size of chiral circular cylinder, the thickness of cylindrical chirodome and the parameters of chiral media, purely circular and linear polarization can be obtained in the far field. Also, the expressions of dyadic Green's function given in this paper can be directly used to analyse the radiation characteristics of cylindrical chirostrip antennas.