An analytic solution is obtained for a plane electromagnetic wave scattering by an infinitely imperfectly conducting cylinder clad by a composite anisotropic chiral sheath. The coating medium is assumed homogeneous. Closed form expressions are derived for the electromagnetic fields in composite anisotropic chiral media. Both TE and TM polarized wave incident normally on the circular cylinder are considered. Numerical results for various values of the parameters are presented and discussed.