An exact solution is presented to the problem of scattering of a plane wave by a chiral semi-elliptic-cylindrical boss located on an infinite perfectly conducting ground plane. The problem is formulated by expressing the incident, reflected, scattered as well as the transmitted electromagnetic fields in terms of appropriate angular and radial Mathieu functions and sets of expansion coefficients. The unknown expansion coefficients can be determined by imposing the appropriate boundary conditions on the surface of the chiral semi elliptical cylinder. Numerical results are presented for radar cross section of semi-elliptic-cylindrical bosses of different chiral material, to show the effects of these on it.