Absorption and emission lines originating from the ν₃ C–H stretching manifold of gas-phase CH₄ were discovered in the high-resolution (R = 25,000) infrared L-band spectrum along the line of sight toward NGC 7538 IRS 9. These observations provide a diagnostic of the complex dynamics and chemistry in a massive star-forming region. The line shapes resemble P Cygni profiles with the absorption and emission components shifted by ~7 km s^-1 with respect to the systemic velocity. Similar velocity components were observed in CO at 4.7 μm, but in contrast to CH₄, the CO shows deep absorption due to a high-velocity outflow as well as absorption at the systemic velocity due to the cold outer envelope. It is concluded that the gas-phase CH₄ abundance varies by an order of magnitude in this line of sight: it is low in the envelope and the outflow (X[CH₄] < 0.4 × 10^-6) and at least a factor of 10 larger in the central core. The discovery of solid CH₄ in independent ground- and space-based data sets shows that methane is nearly entirely frozen onto grains in the envelope. It thus appears that CH₄ is formed by grain surface reactions, evaporates into the gas phase in the warm inner regions of protostellar cores, and is efficiently destroyed in shocks related to outflows.