We extend recent flux-flux autocorrelation function methods for the direct computation of thermal reaction rate constants and unimolecular recombination rates to the case where both reaction and recombination are possible. Rather than a single transition state dividing surface, dividing surfaces are placed on both the reactant (r) and product (p) sides of the intermediate collision complex region. The thermal recombination rate expression then involves a flux cross-correlation function C-rp(t) in addition to the usual autocorrelation function C-rr(t), both of which are computed during a single quantum time propagation. This method is applied to the three-dimensional O + OH reversible arrow H + O-2 (J = 0) reactions, employing parallel computation because of the necessary large basis (2(18) grid points) and long propagation times (2-3 ps). Thermal rate constants (in the absence of recombination effects) are presented for T = 500-2000 K, using the J-shifting approximation to account for nonzero total angular momentum; good agreement is found with experimental measurements of bath forward and reverse rate constants. Collisional recombination by a bath gas is included via the strong collision assumption, and rate constants for the competing O + OH reaction (H + O-2) and recombination (HO2) channels are calculated as a function of collision frequency, i.e., pressure of the bath gas.