We report on crossed-beam experiments and quantum-mechanical calculations performed on the CO(j=0) + H2(j=0) → CO(j=1) + H2(j=0) system. The experimental cross sections determined in the threshold region of the CO(j=0 → j=1) transition at 3.85 cm(-1) show resonance structures in good qualitative agreement with the theoretical ones. These results suggest that the potential energy surface which describes the CO-H2 van der Waals interaction should be reinvestigated for good quantitative agreement.