Rate constants of the prototypical methyl-methyl radical association reaction are calculated on the basis of variational transition-state theory with a variable reaction coordinate and a multifaceted dividing surface. The potential energies required in the Monte Carlo integrations are evaluated directly using the M06 and M06-L density functionals. The rate constants are calculated at the canonical, microcanonical, and E,J-resolved microcanonical levels. The best prediction of rate constants is based on the potential energies calculated by the M06-L density functional; these agree with experimental data quantitatively from 300 to 1000 K. This study shows that density functional theory can be accurate enough for calculating rate constants of reactions with loose transition states, whereas previously only multireference wave function methods, which are more complicated and more expensive, had been demonstrated to be sufficiently accurate. The application of density functional theory for the loose transition states will allow larger and complicated systems to be studied efficiently.