Observations with the Short Wavelength Spectrometer on board the Infrared Space Observatory have led to the first detection of the methyl radical CH3 in the interstellar medium. The ν2 Q-branch at 16.5 μm and the R(0) line at 16.0 μm have been unambiguously detected toward the Galactic center Sagittarius A*. The analysis of the measured bands gives a column density of (8.0+/-2.4)×1014 cm-2 and an excitation temperature of 17+/-2 K. Gaseous CO at a similarly low excitation temperature and C2H2 are detected for the same line of sight. Using constraints on the H2 column density obtained from C18O and visual extinction, the inferred CH3 abundance is (1.3+2.2-0.7)×10-8. The chemically related CH4 molecule is not detected, but the pure rotational lines of CH are seen with the Long Wavelength Spectrometer. The absolute abundances and the CH3/CH4 and CH3/CH ratios are inconsistent with published pure gas-phase models of dense clouds. The data require a mix of diffuse and translucent clouds with different densities and extinctions, and/or the development of translucent models in which gas-grain chemistry, freeze-out, and reactions of H with polycyclic aromatic hydrocarbons and solid aliphatic material are included. Based on observations made with the ISO, a project of the ESA with the participation of the ISAS and NASA, and the SWS, a joint project of the SRON and MPE with contributions from KU Leuven, Steward Observatory, and Phillips Laboratory.