How and where the ocean tides dissipate their energy are long-standing questions that have consequences ranging from the history of the Moon to the mixing of the oceans. Historically, the principal sink of tidal energy has been thought to be bottom friction in shallow seas. There has long been suggestive evidence, however, that tidal dissipation also occurs in the open ocean through the scattering by ocean-bottom topography of surface tides into internal waves, but estimates of the magnitude of this possible sink have varied widely. Here we use satellite altimeter data from Topex/Poseidon to map empirically the tidal energy dissipation. We show that approximately 10(12) watts--that is, 1 TW, representing 25-30% of the total dissipation--occurs in the deep ocean, generally near areas of rough topography. Of the estimated 2 TW of mixing energy required to maintain the large-scale thermohaline circulation of the ocean, one-half could therefore be provided by the tides, with the other half coming from action on the surface of the ocean.