The title reaction was studied at 296 K and 0.38-940 Torr total pressure using a FTIR smog chamber technique. The overall rate constant for reaction of CH₃OCH₂ radicals with O₂ may be written, k₁ = k_RO2 + k_prod, where k_RO2 is the rate constant for peroxy radical production and k_prod is the rate constant for the production of other species from reaction 1. k₁ was measured relative to the pressure independent reaction of CH₃OCH₂ radicals with Cl₂ (k₄). There was no discernible effect of pressure on k₁ in the range 200-940 Torr. Between 200 and 2 Torr total pressure k₁ decreased by approximately a factor of 2. For pressures below 2 Torr k₁ was again independent of pressure. The reaction proceeds via the formation of an activated complex, CH₃OCH₂O₂^#, that is either collisionally stabilized to form the peroxy radical, CH₃OCH₂O₂, or undergoes intramolecular H-atom abstraction followed by decomposition to give two formaldehyde molecules and an OH radical: CH₃-OCH₂ + O₂ ⇌ CH₃OCH₂O₂^#, CH₃OCH₂O₂^# + M → CH₃OCH₂O₂ + M, CH₃OCH₂O₂^# → CH₂OCH₂O₂H^# → 2HCHO + OH. The products from this reaction were studied as a function of total pressure. The molar yield of formaldehyde increased from <2% at 700 Torr total pressure to ∼200% at 0.38 Torr total pressure, while the combined yield of methyl formate and methoxy methylhydroperoxide decreased from ∼100% to 4% over the same pressure range. Fitting the product yields and relative rate data using a modified Lindemann expression gave the following rate constants: k_RO2.0/k₄ = (1-97 ± 0.28) × 10^-19 cm³ molecule^-1, k_RO2.∞/k₄ = 0.108 ± 0.004, and k_prod,0/k₄ = (6.3 ± 0.5) × 10^-2 where k_RO2.0 and k_RO2,∞ are the overall termolecular and bimolecular rate constants for formation of the CH₃OCH₂O₂ radical and k_prod,0 represents the bimolecular rate constant for the reaction of CH₃OCH₂ radicals with O₂ to yield formaldehyde in the limit of low pressure. These data and absolute rate data from the literature were used to derive a rate constant for the reaction of CH₃OCH₂ radicals with Cl₂ of (1.00 ± 0.16) × 10^-10 cm³ molecule^-1 s^-1. The results are discussed in the context of the use of dimethyl ether as an alternative diesel fuel.