We report the development of a new diagnostic capable of measuring plasma ion distributions as a function of all three velocity-space coordinates. The diagnostic makes use of laser-induced fluorescence (LIF) and computer-assisted image reconstruction techniques. LIF yields high-resolution, nonperturbing measurements of one-dimensional distributions that are integrated in two directions through three-dimensional velocity space. Computer tomography allows for the unambiguous determination of the complete ion velocity distribution. In addition to a description of the diagnostic, examples of recovered distributions obtained from experiments are given, and the effects of the major steps in the data processing are discussed.