Gas hydrates are a major component in the organic carbon cycle. Their stability is controlled by temperature, pressure, water chemistry, and gas composition. The bottom‐simulating reflector (BSR) is the primary seismic indicator of the base of hydrate stability in continental margins. Here we use seismic, well log, and core data from the convergent margin offshore NW Borneo to demonstrate that the BSR does not always represent the base of hydrate stability and can instead approximate the boundary between structure I hydrates above and structure II hydrates below. At this location, gas hydrate saturation below the BSR is higher than above and a process of chemical fractionation of the migrating free gas is responsible for the structure I‐II transition. This research shows that in geological settings dominated by thermogenic gas migration, the hydrate stability zone may extend much deeper than suggested by the BSR. Key Points Structure II gas hydrates form below a bottom‐simulating reflector due to thermogenic gas migration and coexist with free gas A chemical fractionation process provokes a transition at the bottom‐simulating reflector from structure II to structure I hydrates Gas hydrate systems sourced by thermogenic fluids can be characterized by more hydrates below than above bottom‐simulating reflectors