Unlike the ideal circular whispering gallery cavities, those without mirror symmetry intrinsically support resonant modes exhibiting chirality which indicates an imbalance between clockwise and counterclockwise wave components. In extreme cases, nearly degenerate pairs of copropagating modes can be found around the chiral exceptional points (EPs) in parameter spaces. The chiral EPs have been studied in various schemes; however, most attention has been focused on the cases with piecewise constant or periodic refractive index profiles. In this Letter, we report the formation of a chiral EP in a gradient-index cavity designed by conformal transformation optics. Here, the mirror symmetry of the cavity is broken solely by its gradient index profile, and the parameter space is constructed with coordinate transformation parameters. We unveil the chirality, nonorthogonality, and complex-square-root topology near the chiral EP, which can be explained by the non-Hermitian model Hamiltonian.