A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2sigma) limit of alpha = (0.9 +/- 4.6) x 10(-4) at lambda = 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(1 + alphae(-r/lambda)).