Three-dimensional seismic reflection data from offshore Mauritania reveal a base hydrate reflection, beneath which are 56 stratigraphically trapped gas accumulations (∼0.08 Gt methane). Only 2 are sealed by the base of the hydrate (∼0.004 Gt methane) and therefore constitute the free gas zone. Some of the stratigraphically trapped gas accumulations are critically pressured. There are also 360 gas chimneys beneath the gas hydrate, but not outside the region covered by it. They are evidence for repetitious leaking from the accumulations. Only 12 of the chimneys terminate at a contemporaneous seabed, showing that methane venting was not significant. Instead, upward resetting of the base hydrate triggered gas dissociation and caused the traps to become charged and critically pressured. Vertical leaking to intermediate, shallower stratigraphic traps or to the gas hydrate itself, where it was reincorporated, occurred once the seal capacity was exceeded. Most (95%) of the free gas is stored stratigraphically and re-migrates in this way, and this trapping mechanism may be typical of fine-grained passive margin continental slopes. Only 5% of the gas is within the free gas zone. The role of recycling of methane between the hydrate and stratigraphic traps has not previously been recognized and represents a store for this greenhouse gas that is not susceptible to changes in ambient conditions.