An algorithm is described for computing rate constants with semi-classical transition state theory (SCTST) formulated by Miller and coworkers. SCTST incorporates non-separable coupling among all degrees of freedom and multi-dimensional quantum mechanical tunneling along the curved reaction path. The algorithm, which is practical for reactants containing dozens of atoms, predicts both microcanonical and canonical rate constants. In addition, the quantum chemistry code CFOUR has been extended to efficiently compute fully-coupled vibrational anharmonicities for transition states at the CCSD(T) level of theory. The new methods are demonstrated for the H2 + OH reaction and the ‘tail-biting’ isomerization of acetylperoxyl radical.