The structure of saturated monolayer methyl nitrite, CH3ONO, on Ag(lll), as determined by reflection-absorption infrared spectroscopy (RAIRS), is presented. Methyl nitrite adsorbs molecularly, monolayer desorption peaks at 122 K, and there is no evidence for thermal decomposition. RAIRS indicates that adsorbed methyl nitrite, at 104 K, is dominated by the cis isomer (>90%) and bonds weakly to Ag through the lone pair electrons of the internal oxygen. From analysis of relative band intensities, we conclude that the C-S plane of adsorbed CH3ONO lies near the surface normal and the N-O bond containing the internal O is tilted similar to 45 degrees from the surface normal. This orientation is consistent with the facile ejection of NO observed in previous photochemistry experiments.