Reports of plumes or patches of methane in the martian atmosphere that vary over monthly time scales have defied explanation to date. From in situ measurements made over a 20-month period by the tunable laser spectrometer of the Sample Analysis at Mars instrument suite on Curiosity at Gale crater, we report detection of background levels of atmospheric methane of mean value 0.69 +/- 0.25 parts per billion by volume (ppbv) at the 95% confidence interval (CI). This abundance is lower than model estimates of ultraviolet degradation of accreted interplanetary dust particles or carbonaceous chondrite material. Additionally, in four sequential measurements spanning a 60-sol period (where 1 sol is a martian day), we observed elevated levels of methane of 7.2 +/- 2.1 ppbv (95% CI), implying that Mars is episodically producing methane from an additional unknown source.