The mechanism and kinetics of chemical vapor deposition of silicon nitride films from a gas-phase mixture of dichlorosilane and ammonia have been studied theoretically by a combination of density functional theory, transition state theory, and quantum Rice-Ramsperger-Kassel theory. Analysis of estimated gas-phase reaction rate constants at typical deposition conditions for single-wafer processing shows a substantial conversion into aminochlorosilane. The dominating bimolecular reaction of a concerted Si-N bond formation and HCl elimination has a much lower activation barrier (similar to 38 kJ/mol) than unimolecular dichlorosilane decomposition (similar to 250-290 kJ/mol). A mechanism of gas-surface reactions has been suggested, with activation energies extrapolated from those of corresponding gas-phase reactions and a uniform pre-exponential Arrhenius factor optimized to fit the experimentally observed film growth rate. Analysis of the resulting gas and surface reaction mechanisms provides insight into the key reaction paths for film growth.