Relative dispersion of a passive scalar plume was investigated in uniformly sheared, nearly homogeneous, turbulent flow with Reλ≈150 using planar laser-induced fluorescence. Mean concentration maps were determined both in the laboratory frame and in a frame attached to the instantaneous center of mass of the plume cross section. The distance-neighbor function had a shape that was compatible with Richardson's expression. The mean square particle separation, two estimates of which were found to be nearly identical, had a streamwise evolution that was consistent with Richardson-Obukhov scaling with a Richardson's constant of g=0.35. Batchelor scaling was also consistent with a wide range of the results.