The quantum-mechanical statistical phase-space theory of Pechukas, Light, and Nikitin is used to calculate the cross sections for the endothermic reaction C++D2→CD++D in the energy range 0-4 eV. The calculated cross section is about two times larger than the experimental results of Maier (1967) and has almost the same energy dependence below 2 eV. The statistical-theory threshold law is predicted to be valid only for a region less than 0.1 eV from threshold. Two different types of dependence of the reaction probability on incident impact parameter are emphasized, and one is used to explain the magnitude of the predicted cross section in this case. The intramolecular isotope effect in C++HD collisions is studied and the CH+/CD+ product ratio is predicted to be 0.92 at 1 eV.