ATMOSPHERIC concentrations of methane, an important greenhouse gas, have increased significantly over the past few decades1,2. Although attention has been focused on anthropogenic sources, data from ice cores show that large changes in atmospheric methane concentrations have occurred over glacial-interglacial time scales, indicating that there is significant variability in natural methane fluxes3,4. The surface waters of the oceans are often supersaturated with methane, which implies that the oceans are a net source, although their contribution to the global methane budget is small relative to other sources4. Here we report high concentrations of methane in the Arabian Sea, and calculate that the flux of methane to the atmosphere is up to five times greater than the previously reported average ocean flux. Methane production is associated with high phytoplankton biomass, which is closely coupled with the monsoon-driven upwelling of nutrient-rich water. We calculate that the Arabian Sea (representing 0.43% of the total surface area of the world's oceans) could account for between 1.3 and 133% of the current estimates of the open-ocean source of methane. Our results do not alter the view that the oceans are a relatively minor source of atmospheric methane, but the magnitude of the methane fluxes from the Arabian Sea and the link with the monsoon suggest that this region may be particularly sensitive to climate change, with a greater potential for feedback responses than its surface area might suggest.