The dynamics of the Cl + HD reaction has been studied by means of time-dependent quantum wave packet calculations on the G3 and BW2 potential energy surfaces. Initial state-specific total reaction probabilities and integral cross sections are calculated, and the thermal rate constant is obtained. The good agreement was shown in the comparison of our integral cross sections with other quantum mechanics calculations on the same PES. The thermal rate constants on the G3 surface are close to the experiment findings. In the case of neglect of spin-orbit coupling in the ab initio calculations of the BW2 surface, the thermal rate constants on the surface are somewhat higher than the experimental measurement. When the spin-orbit coupling is taken into account, the thermal rate constants on the BW2 surface are close to the experiment as well.