Reports of methane detection in the Martian atmosphere have been intensely debated. The presence of methane could enhance habitability and may even be a signature of life. However, no detection has been confirmed with independent measurements. Here, we report a firm detection of 15.5 +/- 2.5 ppb by volume of methane in the Martian atmosphere above Gale Crater on 16 June 2013, by the Planetary Fourier Spectrometer onboard Mars Express, one day after the in situ observation of a methane spike by the Curiosity rover. Methane was not detected in other orbital passages. The detection uses improved observational geometry, as well as more sophisticated data treatment and analysis, and constitutes a contemporaneous, independent detection of methane. We perform ensemble simulations of the Martian atmosphere, using stochastic gas release scenarios to identify a potential source region east of Gale Crater. Our independent geological analysis also points to a source in this region, where faults of Aeolis Mensae may extend into proposed shallow ice of the Medusae Fossae Formation and episodically release gas trapped below or within the ice. Our identification of a probable release location will provide focus for future investigations into the origin of methane on Mars.