The gas-phase reaction between chloromethane and hydrogen proceeds by two channels, Cl- and H-abstraction, and was chosen as a model of asymmetrically substituted polyatomic reactions of type CX3Y + A -> products. The analytical potential energy surface for this reaction was constructed with suitable functional forms to represent vibrational modes, and both channels were independently fitted to reproduce experimental and theoretical information only at the stationary points. The rate constants for the Cl- and H-channels and the overall reaction were calculated using variational transition-state theory with multidimensional tunneling effect over a wide temperature range, 298-3000 K. The Cl-abstraction reaction is preferred until 2100 K, while above this temperature the H-abstraction channel is favored. The theoretical overall rate constants agree with the experimental data in the common temperature range, 500-800 K. with a small curvature of the Arrhenius plot due mainly to the role of the tunneling in the H-abstraction channel. This surface was then used to analyze dynamical features, such as reaction-path curvature, and coupling between the reaction-coordinate and vibrational modes. It was found qualitatively that excitation of the C-Cl and C-H stretching reactive modes enhances the forward rate constants for the Cl- and H-abstraction channels, respectively, and only the Cl-H and H-H stretching modes in the products of the Cl- and H-abstraction reactions, respectively, appear vibrationally excited.