A detailed surface chemistry mechanism is proposed for chemical vapor deposition of diamond films, which extends the growth-by-methyl mechanism proposed by Harris to treat any CHm radical, m=0-3, as a growth monomer. Numerical computations were performed in which the mechanism was coupled to a model for the boundary layer above the substrate, for conditions typical of diamond deposition in an atmospheric-pressure thermal plasma. The predicted linear growth rate increases strongly as the boundary layer thickness δ is decreased, and the results indicate a strong dependence of the diamond growth chemistry on δ. For relatively thick boundary layers (modest velocities of the reactant jet) growth is dominated by CH3. For very thin boundary layers (high velocities) the model predicts that growth is dominated by C. For the transition region where C and CH3 each contribute about 40% to growth, CH2 also contributes about 17%. The carbon conversion efficiency is also predicted to peak in the transition region, and drops sharply for very thin boundary layers.