Recent spectroscopic detections of CH4 in the atmosphere of Mars are the first definitive observations of an organic compound on that planet. The relatively short photochemical lifetime of CH4 (~300 years) argues for a geologically young source. We demonstrate here that low-temperature alteration of basaltic crust by carbon-bearing hydrothermal fluid can produce the required CH4 flux of 1 ¿ 107 moles year-1, assuming conservative values for crustal permeability and oxygen fugacity as implied by Martian basaltic meteorites. The crustal thermal disturbance due to a single dike ~1 ¿ 1 ¿ 10 km intruded during the past 104 years is capable of driving the alteration, if all carbon is supplied by magmatic degassing from a dike with only 50 ppm C. Atmospheric methane strongly suggests ongoing magmatism and hydrothermal alteration on Mars.