Anthropogenic global warming may be accelerated by a positive feedback from the mobilization of methane from thawing Arctic permafrost. There are large uncertainties about the size of carbon stocks and the magnitude of possible methane emissions. Methane cannot only be produced from the microbial decay of organic matter within the thawing permafrost soils (microbial methane) but can also come from natural gas (thermogenic methane) trapped under or within the permafrost layer and released when it thaws. In the Taymyr Peninsula and surroundings in North Siberia, the area of the worldwide largest positive surface temperature anomaly for 2020, atmospheric methane concentrations have increased considerably during and after the 2020 heat wave. Two elongated areas of increased atmospheric methane concentration that appeared during summer coincide with two stripes of Paleozoic carbonates exposed at the southern and northern borders of the Yenisey-Khatanga Basin, a hydrocarbon-bearing sedimentary basin between the Siberian Craton to the south and the Taymyr Fold Belt to the north. Over the carbonates, soils are thin to nonexistent and wetlands are scarce. The maxima are thus unlikely to be caused by microbial methane from soils or wetlands. We suggest that gas hydrates in fractures and pockets of the carbonate rocks in the permafrost zone became unstable due to warming from the surface. This process may add unknown quantities of methane to the atmosphere in the near future.