The influence of quantum mechanics on the dynamics of chemical reactions is unknown for many processes in chemistry. Chemical reaction dynamics are often well described by quasiclassical motion of the atoms on quantum mechanical Born-Oppenheimer potential energy surfaces. Here we present a dynamic isotope effect in a nucleophilic substitution reaction experiment that can only be explained by quasiclassical trajectory simulations for reactants containing deuterium atoms, but not when hydrogen atoms are involved. The calculated energy- and angle-differential cross sections are compared to experimental crossed-beam velocity map imaging data, which show significantly more forward scattering for hydrogenated compared to deuterated reactants. Quantum scattering calculations in reduced dimensions explain this by an increased reaction probability for large total angular momentum, a feature that is not captured in the quasiclassical approach.