We present a reduced dimensionality quantum dynamics study of the hydrogen abstraction reaction on a semirigid (111) diamond surface, C-d + H-2(v,j,m) --> CdH + H. A nine-dimensional potential energy surface is developed by combining a London-Eyring-Polanyi-Sato potential based on ab initio data with nonbonded and surface interactions. Four reactive degrees of freedom are treated explicitly using a recently developed wave packet approach in a real L-2 basis, and the total reaction probabilities for initial states v = 0-1, j = 0-11, and m = 0-4 are calculated over a large total energy range. The remaining five degrees of freedom are treated using energy-shift approximations, and the full cumulative reaction probability is obtained and from it the full thermal rate constant. Comparison with conventional transition state theory indicates that at 300 K tunneling accounts for 90% of the rate constant and remains significant even at high temperatures. Dynamical corrections to transition state theory become important above 1000 K. At 1200 K the tunneling and dynamical corrections nearly cancel each other and the transition state theory rate constant agrees very well with quantum rate constant. The coupling of surface and reactive modes has only a minor, less then 15%, effect on the rate constants, provided that the energetics for the relaxed surface are incorporated into the potential. The thermal rate for H abstraction from diamond, obtained from detailed balance, is in good agreement with experimental data. Under typical chemical vapor deposition conditions the thermal rate for H abstraction by diamond active sites is found to be 100 slower than the rate of competitive reaction, H addition to diamond active sites.