Initially state-selected cross sections and thermal rate constants for the reaction CN+H-2--> HCN+H have been calculated using a mixed quantum-classical method: the vibrations of the two reagents are treated quantum mechanically by means of an exact solution of the time-dependent Schrodinger equation, while translational and rotational motions are treated classically. Coupling between quantum and classical degrees of freedom is realized within an effective Hamiltonian approach.