Gravity is measured presently on the sea surface and on the sea floor. Surface gravity suffers from loss of resolution over the deep ocean because the perturbing source masses are far from the observer. Bottom measurements recover this resolution, but suffer from poor coverage because of the time needed for each measurement. We have constructed a gravimetry system that combines the rapid data collection capability of a moving platform with the high resolution gained by locating the observations near the bottom. This gravity sensor is tethered to a ship and towed just above the sea floor. The instrument consists of a LaCoste and Romberg shipboard gravity meter modified to fit inside a pressure case that is mounted on a platform designed for towing stability. We have tested it in a survey in the San Diego Trough, a 1000-m-deep sedimented valley in the Pacific Ocean in the California continental borderlands. Multiple gravity tracklines collected there at a depth of 935 m show a resolution of a few tenths of a mGal. The new instrument will be useful for surveys of features whose lateral extent is equal to or less than the ocean depth.