The transition-state wave packet method of Zhang and Light [J. Chem. Phys. 104, 6184 (1996)] for the direct calculation of cumulative reaction probabilities is implemented in the Chebyshev order domain to take advantage of exactness and efficiency of the Chebyshev propagator. Numerical testing for three-dimensional H+H-2 reactive scattering (J=0) confirms the accuracy and efficiency of the proposed algorithm. This new implementation is then used to compute the cumulative reaction probability of the Li+HF-->LiF+H reaction (J=0) up to 0.65 eV. It is found that the latter reaction is dominated in low energy region by numerous narrow resonances.