A state-to-state dynamics study was performed for the first time for asymmetrically substituted reactions of the type H + CX3Y --> products, and was applied to the H + CH3Cl gas-phase hydrogen abstraction reaction, analyzing the influence of CH3Cl reactant vibrational stretching and bending excitations. Quasi-classical trajectory calculations were performed on an analytical potential energy surface constructed previously by our group. The strong coupling between different vibrational modes in the entry channel makes the reaction non-adiabatic and the reactant vibrational excitation increases the reactivity of the vibrational ground-state by factors of approximately 2-3 depending on the excited mode. While the H2 and CH2Cl products appear with similar moderate amounts of internal energy, about 25% of the total available energy, most of this energy appears as translational energy, and the reactant vibrational excitation has little influence. The two products appear vibrationally cold, and in the case of the H2 product, also rotationally cold. The product angular distribution is predominantly sideways-backward, the sideways component increasing with the vibrational excitation of the H2 product. The reactant vibrational excitations have little effect on this behaviour. Finally, comparison with theoretical results for the analogue H + CH4 reaction shows that the dynamic behaviour of the two reactions is similar, with the chlorine substituent effect being small or negligible.