In this Letter are presented three-dimensional quantum mechanical cross sections for the title reaction, as calculated for the ab initio potential energy surface of Urban, Jaquet, and Staemmler. The calculations were done within the coupled-states approximation. It is shown that not only are the J=0 probabilities affected by numerous sharp resonances but even the energy-dependent cross sections, for which such resonances are expected to be smoothed out, are characterized by a rich resonance structure. This is the first time that such oscillatory integral cross sections have been obtained for a chemical exchange process. From comparison with quasi-classical-trajectory results, it is shown that the reaction is dominated by quantum effects to the extent that the quasi-classical-trajectory calculations sometimes become irrelevant.