A density functional theory (DFT) study of the reaction of dibenzofuranyl radical with oxygen molecule has been made. The geometries, energies, and vibrational frequencies of the reactant, transition states, intermediates, and products have been calculated at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level of theory. The initial reaction of dibenzofuran (DBF) with molecular oxygen results in the formation of the 1-dibenzofuranylperoxy radical. The stability of this adduct toward decomposition at low to intermediate temperatures results in it undergoing several possible rearrangements. The lowest energy pathway with a barrier of 24.2 kcal/mol involves a rearrangement to the 1,1-dioxadibenzofuran radical. The next lowest energy pathway involves fission of the O-O linkage whose reaction energy was found to be 37.6 kcal/mol. Transition state theory (TST) calculations indicate that the lowest energy pathway should predominate at temperatures up to about 1200 K. Two other unimolecular reaction pathways with barriers of 45.5 and 91.1 kcal/mol have also been discovered. The latter pathway leads to the formation of a para-quinone (dibenzofuran quinone) which has been detected experimentally in the low-temperature oxidation of DBF [Marquaire, P. M.; Worner, R.; Rambaud, P.; Baronnet, F. Organohalogen Compd. 1999, 40, 519]. Our quantum calculations, however, do not support this latter pathway to quinone formation. Instead, the quinone is most probably formed as a consequence of recombination of the 1-dibenzofuranyloxy radical (produced by peroxy fission) with an O atom in the para position. Each of the unimolecular reaction pathways have been subjected to detailed quantum chemical investigation and transition states and intermediates leading to the final products (principally CO, CO2, and C2H2 with traces of benzofuran and benzene) have been identified. For certain stable intermediates, their possible reactions with molecular oxygen have been further investigated quantum chemically. The present work therefore presents a detailed quantum chemical investigation of the reaction pathways in the low-temperature oxidation mechanism of DBF. Since the dibenzofuran moiety is present in the polychlorinated DBFs, our conclusions should be generally applicable to this family of compounds.