The differential cross section for the H + D(2) --> HD + D reaction has been measured using a technique called reaction product imaging. In this experiment, a photolytically produced beam of hydrogen (H) atoms crossed a beam of cold deuterium (D(2)) molecules. Product D atoms were ionized at the intersection of the two particle beams and accelerated toward a position-sensitive detector. The ion images appearing on the detector are two-dimensional projections of the three-dimensional velocity distribution of the D atom products. The reaction was studied at nominal center-of-mass collision energies of 0.54 and 1.29 electron volts. At the lower collision energy, the measured differential cross section for D atom production, summed over all final states of the HD(v,J) product, is in good agreement with recent quasi-classical trajectory calculations. At the higher collision energy, the agreement between the theoretical predictions and experimental results is less favorable.