The infrared spectrum of the weakly bound complex CO-paraH(2), which accompanies the fundamental band of CO in the 4.7 mu m region, has been recorded at high resolution (0.005 cm(-1)) using a long-path (200 m), low-temperature (48 K), absorption cell. A total of 135 transitions, constituting almost all of the observed lines, has been rotationally assigned in terms of 44 discrete quantum states of the complex, and the positions of these energy levels have been determined to high accuracy (< 0.001 cm(-1)) for both the nu(CO) = 0 and 1 vibrational states. The binding energy of the complex, relative to the zero-point level, was determined to be about 22 cm(-1). Predicted microwave and millimeter wave frequencies are given for the pure rotational spectrum of CO-paraH(2). The energy level pattern derived here provides the information needed to make precise determinations of the CO-H-2 intermolecular potential energy surface in the attractive region. However, determination of the dependence of this surface on the orientation of H-2 within the complex will have to await the analysis of the more complicated spectrum of CO-orthoH(2).