First quasiclassical trajectory calculations have been carried out for the C(3P)+OH(X 2Pi)-->CO(X 1Sigma+)+H(2S) reaction using a recent ab initio potential energy surface for the ground electronic state, X 2A', of HCO/COH. Total and state-specific integral cross sections have been determined for a wide range of collision energies (0.001-1 eV). Then, thermal and state-specific rate constants have been calculated in the 1-500 K temperature range. The thermal rate constant varies from 1.78x10(-10) cm3 s-1 at 1 K down to 5.96x10(-11) cm3 s-1 at 500 K with a maximum value of 3.39x10(-10) cm3 s-1 obtained at 7 K. Cross sections and rate constants are found to be almost independent of the rovibrational state of OH.