The effect of pressure on chemical interactions in molecular mixtures is important for problems spanning fundamental chemistry, planetary science, and materials science. Diamond-anvil cell studies reveal pressure-induced chemistry in the CH4-H-2 system. The system, which has no known compounds at ambient conditions, formed four molecular compounds, CH4(H-2)(2), (CH4)(2)H-2, CH4(H-2)(4), and CH4H2, at pressures up to 10 gigapascals. These have been characterized by synchrotron single-crystal x-ray diffraction, polycrystalline x-ray diffraction, Raman spectroscopy, and visual observation. Although CH4(H-2)(2) crystallizes in the MgZn2-type, hexagonal Laves phase structure, (CH4)H-2 has a body-centered tetragonal structure that is similar to that of Al2Cu. The 1:1 and 1:2 compounds are stable to at least 30 gigapascals.