Thwaites Glacier is one of the fastest-changing ice-ocean systems in Antarctica^1-3. Much of the ice sheet within the catchment of Thwaites Glacier is grounded below sea level on bedrock that deepens inland⁴, making it susceptible to rapid and irreversible ice loss that could raise the global sea level by more than half a metre^2,3,5. The rate and extent of ice loss, and whether it proceeds irreversibly, are set by the ocean conditions and basal melting within the grounding-zone region where Thwaites Glacier first goes afloat^3,6, both of which are largely unknown. Here we show-using observations from a hot-water-drilled access hole-that the grounding zone of Thwaites Eastern Ice Shelf (TEIS) is characterized by a warm and highly stable water column with temperatures substantially higher than the in situ freezing point. Despite these warm conditions, low current speeds and strong density stratification in the ice-ocean boundary layer actively restrict the vertical mixing of heat towards the ice base^7,8, resulting in strongly suppressed basal melting. Our results demonstrate that the canonical model of ice-shelf basal melting used to generate sea-level projections cannot reproduce observed melt rates beneath this critically important glacier, and that rapid and possibly unstable grounding-line retreat may be associated with relatively modest basal melt rates.