This paper proposes rational Chebyshev graph filters to approximate step graph spectral responses with arbitrary precision, which are of interest in graph filter banks and spectral clustering. The proposed method relies on the well-known Chebyshev filters of the first kind and on a domain transform of the angular frequencies to the graph frequencies. This approach identifies in closed-form the filter coefficients, hence it avoids the costs of solving a nonlinear problem. Rational Chebyshev graph filters improve the control on the ripples in the pass- and stop-band and on the transition decay. Numerical experiments show the proposed approach approximates better ideal step responses than competing alternatives and reaches the performance of the ideal filters in compressive spectral clustering.