A type of chemical reaction characterized by a reaction path proceeding over an energy barrier (a ridge of the potential energy surface) but not through a saddle point is described. A method of computation of rate constants for such "over-the-ridge" reactions is developed on the basis of RRKM and transition state theories. Formulas and computational procedures are presented for the cases of microscopic energy-dependent rates of unimolecular reactions and the thermally averaged rates of unimolecular or bimolecular reactions. This method is applied to compute the branching fraction of the CO-producing channel (channel 1c) of the reaction of 0 atoms with CH3 radicals. A quantum chemical computational study of the potential energy surface (PES) of the decomposition of CH3O was performed using UHF, UMP2, QCISD, and B3LYP methods as well as single-point G2 and CBS-Q energy calculations. The results demonstrate that the products of the reaction channel 1c are formed in a process characterized by trajectories in coordinate space that proceed over a potential energy ridge but not through a saddle point. The method developed in this work was used to calculate the microscopic energy-dependent rate constants of the decomposition of CH3O and the branching fraction of the CO-producing reaction channel (1c). The calculated values of the channel 1c fraction, 4-7% (depending on the potential energy surface used), although lower than the experimental values, overlap in their range of uncertainties with the experiments at the lower end (15 +/- 3% and 18 +/- 4%) of the reported scope of the experimental results which range from 15 +/- 3% to 40 +/- 10%.