Dimethyl sulfoxide (DMSO) is the major sulfur-containing constituent of the Marine Boundary Layer. It is a significant source of H2SO4 aerosol/particles and methane sulfonic acid via atmospheric oxidation processes, where the mechanism is not established. In this study, several new, low-temperature pathways are revealed in the oxidation of DMSO using CBS-QB3 and G3MP2 multilevel and B3LYP hybrid density functional quantum chemical methods. Unlike analogous hydrocarbon peroxy radicals the chemically activated DMSO peroxy radical, [CH3S(=O)CH2OO*]*, predominantly undergoes simple dissociation to a methylsulfinyl radical CH3S*(=O) and a Criegee intermediate, CH2OO, with the barrier to dissociation 11.3 kcal mol(-1) below the energy of the CH3S(=O)CH2* + O2 reactants. The well depth for addition of O2 to the CH3S(=O)CH2 precursor radical is 29.6 kcal mol(-1) at the CBS-QB3 level of theory. We believe that this reaction may serve an important role in atmospheric photochemical and irradiated biological (oxygen-rich) media where formation of initial radicals is facilitated even at lower temperatures. The Criegee intermediate (carbonyl oxide, peroxymethylene) and sulfinyl radical can further decompose, resulting in additional chain branching. A second reaction channel important for oxidation processes includes formation (via intramolecular H atom transfer) and further decomposition of hydroperoxide methylsulfoxide radical, *CH2S(=O)CH2OOH over a low barrier of activation. The initial H-transfer reaction is similar and common in analogous hydrocarbon radical + O2 reactions; but the subsequent very low (3-6 kcal mol(-1)) barrier (14 kcal mol(-1) below the initial reagents) to beta-scission products is not common in HC systems. The low energy reaction of the hydroperoxide radical is a beta-scission elimination of *CH2S(=O)CH2OOH into the CH2=S=O + CH2O + *OH product set. This beta-scission barrier is low, because of the delocalization of the *CH2 radical center through the -S(=O) group, to the -CH2OOH fragment in the transition state structure. The hydroperoxide methylsulfoxide radical can also decompose via a second reaction channel of intramolecular OH migration, yielding formaldehyde and a sulfur-centered hydroxymethylsulfinyl radical HOCH2S*(=O). The barrier of activation relative to initial reagents is 4.2 kcal mol(-1). Heats of formation for DMSO, DMSO carbon-centered radical and Criegee intermediate are evaluated at 298 K as -35.97 +/- 0.05, 13.0 +/- 0.2 and 25.3 +/- 0.7 kcal mol(-1) respectively using isodesmic reaction analysis. The [CH3S*(=O) + CH2OO] product set is shown to form a van der Waals complex that results in O-atom transfer reaction and the formation of new products CH3SO2* radical and CH2O. Proper orientation of the Criegee intermediate and methylsulfinyl radical, as a pre-stabilized pre-reaction complex, assist the process. The DMSO radical reaction is also compared to that of acetonyl radical.