The reaction of 3CH2 with 3O2 is of fundamental importance in combustion, and the reaction is complex as a result of multiple extremely exothermic product channels. In the present study, direct dynamics simulations were performed to study the reaction on both the singlet and triplet potential energy surfaces (PESs). The simulations were performed at the UM06/6-311++G(d,p) level of theory. Trajectories were calculated at a temperature of 300 K, and all reactive trajectories proceeded through the carbonyl oxide Criegee intermediate, CH2OO, on both the singlet and triplet PESs. The triplet surface leads to only one product channel, H2CO + O(3P), while the singlet surface leads to eight product channels with their relative importance as CO + H2O > CO + OH + H ∼ H2CO + O(1D) > HCO + OH ∼ CO2 + H2 ∼ CO + H2 + O(1D) > CO2 + H + H > HCO + O(1D) + H. The reaction on the singlet PES is barrierless, consistent with experiment, and the total rate constant on the singlet surface is (0.93 ± 0.22) × 10-12 cm3 molecule-1 s-1 in comparison to the recommended experimental rate constant of 3.3 × 10-12 cm3 molecule-1 s-1. The simulation product yields for the singlet PES are compared with experiment, and the most significant differences are for H, CO2, and H2O. The reaction on the triplet surface is also barrierless, inconsistent with experiment. A discussion is given of the need for future calculations to address (1) the barrier on the triplet PES for 3CH2 + 3O2 → 3CH2OO, (2) the temperature dependence of the 3CH2 + 3O2 reaction rate constant and product branching ratios, and (3) the possible non-RRKM dynamics of the 1CH2OO Criegee intermediate.