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By exploiting a rigorous variational formulation, we point out the main effects of a chiral cover on a cavity backed microstrip patch antenna. A hybrid finite element-boundary integral method is employed to solve numerically the electromagnetic problem modeled by a variational functional. The dependence of the resonance frequency on the cover thickness and on the chirality admittance of the material is first investigated. In more detail, it is demonstrated that a chiral cover permits reducing the antenna dimensions, compared to an isotropic one, for a fixed working frequency. Then, through several numerical examples, we also investigate the variation of gain properties, cross-polarization levels, radiation resistance, radiation efficiency, and radar cross-section.