Chemical reactions of methyl radicals on (100) diamond surfaces have been investigated theoretically. Quantum-mechanical calculations at the PM3 semiempirical level were performed on a series of small- and large-size clusters to explore possible reaction steps responsible for diamond growth at conditions typical of chemical vapor deposition. Among a variety of possible chemisorption sites considered, surface dimer radicals not only were the most favorable on kinetic grounds but appeared to be the only type capable of sustaining the subsequent incorporation of adsorbed methyl groups into the diamond lattice, Surface migration of H atoms, radical sites, and chemisorbed CH groups proved to be important for diamond growth. A new reaction mechanism of diamond (100) growth from methyl radicals is proposed which offers a plausible explanation for the experimentally observed fast and smooth growth of diamond surfaces. The mechanism consists of two principal features, conversion of dimer sites into bridge sites and surface migration of bridge sites toward continuous bridge chains; it does not require any particular order of dimer formation but establishes the governing role of surface diffusion.