A general solution is obtained to a canonical problem of the reflection and refraction of an arbitrary shaped beam by using a uniaxially anisotropic chiral slab.The reflected,internal as well as refracted shaped beams are expanded in terms of cylindrical vector wave functions,and the expansion coefficients are determined by using the boundary conditions and method of moments procedure.As two typical examples,the normalized field intensity distributions are evaluated for a fundamental Gaussian beam and Hermite-Gaussian beam,and some propagation properties,especially the negative refraction phenomenon,are discussed briefly.