Abstract: The reaction of chlorine atom Cl(^2P) (Cl(^2P_3/2) and Cl^*(^2P_1/2)) with D_2 was investigated at collision energy from 4.5 kcal/mol to 6.5 kcal/mol with a high-resolution crossed molecular beam apparatus using the technique of D-atom Rydberg tagging detection. The contribution from the spin-orbit excited reaction Cl^*(^2P_1/2)+D_2, which is prohibited by Born-Oppenheimer (BO) approximation, was observed. Collision-energy dependence of differential cross sections (DCSs) near the backward scattering direction was measured. The BO-forbidden reaction Cl^*+D_2 was found to be dominant at lower collision energy. As collision energy increases, reactivity of BO-allowed reaction Cl+D_2 increases much faster than that of BO-forbidden reaction and becomes dominant at higher collision energy. Our experiment indicates that the additional energy of spin-orbit excitation in Cl^* facilitates BO-forbidden reaction to pass through the barrier at lower collision energy, while BO approximation is still valid at collision energy near and above the reaction barrier. This tendency of reactivity of Cl/Cl^*+D_2 is similar to the isotopic reaction of Cl/Cl^*+H_2.