The NASA/Deutsches Zentrum f¿r Luft- und Raumfahrt (DLR) satellite gravity mission Gravity Recovery and Climate Experiment (GRACE), launched in March 2002, will map the Earth's gravity field at scales of a few hundred kilometers and greater every 30 days. We describe a method of using those gravity measurements to estimate temporal variations in deep ocean currents. We examine the probable accuracy of the current estimates by constructing synthetic GRACE data, based in part on output from an ocean general circulation model. We ignore the possible contamination caused by short-period gravity signals aliasing into the 30-day solutions. We conclude that in the absence of aliasing, GRACE should be able to recover the 30-day variability of midlatitude currents at a depth of 2 km with an error of about 6--15% in variance when smoothed with 500--700 km averaging radii.