The floating ice shelf of Petermann glacier interacts directly with the ocean and is thought to lose at least 80% of its mass through basal melting. Based on three opportunistic ocean surveys in Petermann Fjord we describe the basic oceanography: the circulation at the fjord mouth, the hydrographic structure beneath the ice shelf, the oceanic heat delivered to the under-ice cavity, and the fate of the resulting melt water. The 1100 m deep fjord is separated from neighboring Hall Basin by a sill between 350 and 450 m deep. Fjord bottom waters are renewed by episodic spillover at the sill of Atlantic water from the Arctic. Glacial melt water appears on the northeast side of the fjord at depths between 200 m and that of the glacier’s grounding line (about 500 m). The fjord circulation is fundamentally three-dimensional; satellite imagery and geostrophic calculations suggest a cyclonic gyre within the fjord mouth, with outflow on the northeast side. Tidal flows are similar in magnitude to the geostrophic flow. The oceanic heat flux into the fjord appears more than sufficient to account for the observed rate of basal melting. Cold, low-salinity water originating in the surface layer of Nares Strait in winter intrudes far under the ice. This may limit basal melting to the inland half of the shelf. The melt rate and long-term stability of Petermann ice shelf may depend on regional sea ice cover and fjord geometry, in addition to the supply of oceanic heat entering the fjord.