Ocean‐driven melting of ice shelves is a primary mechanism for ice loss from Antarctica. However, due to the difficulty in accessing the sub‐ice shelf ocean cavity, the relationship between ice shelf melting and ocean conditions is poorly understood, particularly near the grounding zone, where the ice transitions from grounded to floating. We present the first borehole oceanographic observations from the grounding zone of the Ross Ice Shelf, Antarctica’s largest ice shelf by area. Contrary to predictions that tidal currents near grounding zones mix the water column, we found that Ross Ice Shelf waters were vertically stratified. Current velocities at middepth in the ocean cavity did not change significantly over measurement periods at two different parts of the tidal cycle. The observed stratification resulted in low melt rates near this portion of the grounding zone, inferred from phase‐sensitive radar observations. These melt rates were generally <10 cm/year, which is lower than average for the Ross Ice Shelf (~20 cm/year). Melt rates may be higher at portions of the grounding zone that experience higher subglacial discharge or stronger tidal mixing. Stratification in the cavity at the borehole site was prone to diffusive convection as a result of ice shelf melting. Since diffusive convection influences vertical heat and salt fluxes differently than shear‐driven turbulence, this process may affect ice shelf melting and merits further consideration in ocean models of sub‐ice shelf circulation.