We investigated the reaction of methyl formate, HC(O)OCH3, with hydrogen atoms in solid para-hydrogen (p-H2) at 1.74 and 3.3 K with infrared absorption spectroscopy. Hydrogen atoms were produced either upon direct photolysis of HC(O)OCH3 at 193 nm or upon irradiation of Cl2, codeposited with HC(O)OCH3 in p-H2, with light at 365 nm to produce Cl atoms that react with the p-H2 host via the reaction Cl + H2 (ν = 1) → HCl + H induced by subsequent IR irradiation of the p-H2 matrix. We assigned lines at 1785.2, 1170.6, 1104.6, and 879.4/880.5 cm-1 and five additional weak lines to the methoxy carbonyl radical, •C(O)OCH3, and three weak lines at 1751.3, 1152.9, and 994.4/996.8 cm-1 to the formyloxy methyl radical, HC(O)OCH2•, according to the consideration of possible reactions, correlated variations in intensities after each experimental step, and comparison of observed vibrational wavenumbers and IR intensities with values predicted with the B3LYP/aug-cc-pVTZ method. Unlike most reported H-atom diffusion tunneling reactions, the reaction H + HC(O)OCH3 in solid p-H2 at 3.3 K was found to diminish rapidly after IR irradiation, but, similar to reactions of H + N2O and H + HC(O)OH, this reaction was reinitiated when the matrix temperature was decreased from 4.0 K to 1.5 K. We confirmed that the method used to generate the mobile H atoms does not affect the subsequent chemistry. A possible reaction mechanism and the role of this reaction in dark interstellar clouds are discussed.