Sudden ozone depletion events in the marine boundary layer are associated with jumps in the CH3Br mixing ratio, but current models of atmospheric chemistry explain neither the ozone depletion nor the CH3Br spikes. We have used ab initio theory to predict the forward and reverse rate constants for the competing hydrogen abstraction and homolytic substitution (S(H)2) channels of the title reactions. Including the spin-orbit stabilization of the transition structures increases the rate constants by factors between 1.3 and 49. For the atmospherically relevant case of CH3I, our findings suggest that the hydrogen abstraction and homolytic substitution reactions are competitive. The predicted branching fraction to CH3Br is about 13%.