Stabilized linear inverse theory is applied to the problem of determining the topography of a sub-surface density anomaly from Bouguer gravity observations. The topography is assumed to take the form of a step function in two dimensions, and model predictions are compared directly with the raw data (no smoothing or interpolation is necessary). The concept of resolving power, as introduced by Backus and Gilbert (1970), is extended to problems with fixed linear constraints. The nonuniqueness characteristic of gravity data proves to be conveniently represented by the resolving kernels and poses no problem of numerical instability or poor convergence even where data are sparse. The method is applied to gravity data for Chuckwalla Valley, California, a sedimentary basin with positive gravity anomaly near the center. Although resolution is generally poor, a rather pronounced peak in the basement topography is well resolved and is the cause of the positive anomaly. A single constraint imposed by the depth to basement in one well improves the resolving power of the data significantly.