A four-dimensional potential energy surface has been calculated for the long-range interaction between rigid CN(X) and rigid H-2(X). Electronic structure calculations were performed using single-reference wave function with singles and doubles configuration interaction. Davidson and counterpoise corrections were applied. The atomic orbital basis set was of avtz quality with f-type basis functions removed. The interaction energy at a grid of 865 points was fit by a standard expression in terms of the two in-plane angles, the dihedral angle, and the distance between the diatoms' centers of mass. This fit facilitated examination of the surface and calculation of vibrational eigenstates. The potential exhibits two distinct minima: linear H-H...N-C and T-shaped H-2...C-N, 100 and 68 cm(-1) below the CN + H-2 dissociation asymptote, respectively. Bound states for CN-H-2 and CN-D-2 were calculated for zero total angular momentum (J=0, ignoring spin). Approximate calculations for levels with \K\>0 (where K is the body-fixed projection of J) are also reported. States correlating with j =1 H-2/D-2 were found to be more deeply bound than those that correlate with j = 0 H-2/D-2. The binding energies of CN-orthoH(2) and CN-paraD(2) are predicted to be 26 and 34 cm(-1), respectively. These values are in reasonable agreement with a recent spectroscopic determination from this laboratory. Nuclear wave functions show that the average geometry changes dramatically on excitation of the intermolecular vibrations.