The collision energy dependence of the reaction cross section and the rate constants as a function of the temperature in the range 200-550 K have been determined for the Cl + H-2 and Cl + D-2 reactions by quasiclassical trajectory (QCT) calculations on a new ab initio potential energy surface (PES) by Truhlar and co-workers. For the two reactions, there is a fairly general good agreement between the calculated rate constants and the experimental determinations. The kinetic isotope effect, defined as the ratio of the rate constants for both H-2 isotopomers at a given temperature, is also very well accounted for. However, the QCT rate constants for the Cl + H-2 system are somewhat larger than the measurements, especially at low temperatures, which might indicate that the collinear barrier given by this PES is probably too low.