The sensitive Fluorescence Assay by Gas Expansion (FAGE) method has been used to detect methyl peroxy (CH₃O₂) and hydroperoxyl (HO₂) radicals after their conversion by titration with excess NO to methoxy (CH₃O) and hydroxyl (OH) radicals, respectively, to study the kinetics of the reaction of CH₃O₂ + HO₂ radicals. The rate coefficient of the reaction was measured in the Highly Instrumented Reactor for Atmospheric Chemistry (HIRAC) at 1000 mbar of synthetic air at T = 268–344 K, selectively detecting both radicals. Using a numerical model to fit both CH₃O₂ and HO₂ radical temporal decays globally at each temperature investigated, rate coefficients for the reaction have been obtained. The room temperature rate coefficient was found to be k_CH3O2 +HO2(295 K) = (4.6 ± 0.7) × 10⁻¹² molecule⁻¹ cm³ s⁻¹ (2σ errors) and the temperature dependence of the rate coefficient can be characterized in Arrhenius form by k_{CH3O2 + HO2}(268 K < T < 344 K) = (5.1 ± 2.1) × 10⁻¹³ × exp((637 ± 121)/T) cm³ molecule⁻¹ s⁻¹. The rate coefficients obtained here are 14%–16% lower than the literature recommended values with an uncertainty which is reduced significantly compared to previous reports.