The reaction of the methoxy radical with O-2 is the prototype for the reaction of a range of larger alkoxy radicals with O-2 in the lower atmosphere. This reaction presents major challenges to quantum chemistry, with CCSD(T) overpredicting the barrier height by about 7 kcal/mol in the complete basis set limit. CCSD(T) calculations also indicate that the CH3OOO center dot analog of the HOOO center dot radical is energetically unstable with respect to CH3O center dot + O-2, a finding that seems unlikely. The previous successful prediction of the barrier height using CCSD(T)/cc-pVTZ energies at CASSCF/6-311G(d,p) geometries is shown to rely on the use of a metastable Hartree-Fock reference wave function. The performance of several density functionals is explored and B3LYP is selected to examine the role of tunneling, including the competition between small curvature tunneling (SCT) and large curvature tunneling (LCT). SCT is found to be sufficient to describe tunneling, in contrast to the typical findings for bimolecular hydrogen-abstraction reactions. The previously proposed mechanism of a cyclic transition state yields rate constants for CH3O center dot + O-2 that faithfully reproduces the experimentally derived Arrhenius pre-exponential term. Predictions of the branching ratios for the competing reactions CH2DO center dot + O-2 -> CHDO + HO2 (la) and CH2DO center dot + O-2 -> CH2O + DO2 (lb) are also in good agreement with experiment.