The uniaxial chiral medium, which is a modification of the well-studied reciprocal chiral material, can be created by embedding microscopic metal helices in an isotropic host medium in such a way that the axes of all helices are oriented parallel to a fixed direction but distributed in random locations. In the present investigation, based on the concept of cylindrical vector wave functions in this class of medium, electromagnetic scattering by a uniaxial chiral circular cylinder in the proximity of a PEC plane is rigorously formulated by eigenfunction expansion approach. Formulation of this problem is greatly facilitated by using the image theory of bianisotropic object in the presence of a PEC plane to replace the PEC by an image object with constitutive parameters of image forms. Numerical results indicate the phenomena of backscattering enhancement and polarization transformation phenomenon would occur, simultaneously.