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A state-equation approach is developed to tackle a fiber-reinforced plastic composite (FRPC) cylinder coated by chiral media. This cylinder can be treated as consisting of multilayered bi-isotropic and anisotropic materials. As the chiral coating is properly designed, the backscattering of the linearly polarized plane wave almost disappears in some specific frequency bands. Numerical results of the monostatic echo widths show that a high invisible characteristic of the cylinder can be obtained by appropriately selecting the chiral layer thickness, chiral impedance, chiral nonreciprocity, chirality, and cylinder radius. It is also found that, with the presence of the chiral coating, the bistatic echo widths may be greatly reduced except in the forward scattering direction. However, cross-polarized penetrated fields occur owing to the chiral coating. Adding an interior metal coating is suggested to enhance the shielding performance without sacrificing the invisible property of the cylinder.