Electron energy loss spectra in CH₃I reveal the excitation of the nν₃ and ν₁ + nν₃ progressions near threshold, where ν₃ is the C-I stretch and ν₁ the symmetric CH₃ stretch. Relative elastic and vibrationally inelastic cross sections have been measured as a function of electron energy at 135°. They exhibit many sharp structures at the nν₃, 1ν₁ and 2ν₁ thresholds. A threshold peak is observed for the excitation of the fundamental 1ν₃, but only weak threshold peaks are observed for the higher overtones. The shapes of the cross sections including the sharp structures are well reproduced by a quasiclassical R-matrix resonance theory with non-local potentials. Thermal population of the 1ν₃ level permitted the measurement of the superelastic cross section.