We have determined the far-field beam profiles of an initially Gaussian laser beam that traverses a thin slab of nonlinear-optical material in which the spatial distribution of the refractive nonlinearity is anisotropic by an expansion in terms of elliptical Gaussian functions. In marked contrast to the annular structures observed with isotropic media, it is shown that the transmitted beam breaks into two beams in the far field. This nonlinear beam-splitting behavior has been confirmed experimentally.