Quantum dynamical processes near the energy barrier that separates reactants from products influence the detailed mechanism by which elementary chemical reactions occur. In fact, these processes can change the product scattering behaviour from that expected from simple collision considerations, as seen in the two classical reactions F + H(2) --> HF + H and H + H(2) --> H(2) + H and their isotopic variants. In the case of the F + HD reaction, the role of a quantized trapped Feshbach resonance state had been directly determined, confirming previous conclusions that Feshbach resonances cause state-specific forward scattering of product molecules. Forward scattering has also been observed in the H + D(2) --> HD + D reaction and attributed to a time-delayed mechanism. But despite extensive experimental and theoretical investigations, the details of the mechanism remain unclear. Here we present crossed-beam scattering experiments and quantum calculations on the H + HD --> H(2) + D reaction. We find that the motion of the system along the reaction coordinate slows down as it approaches the top of the reaction barrier, thereby allowing vibrations perpendicular to the reaction coordinate and forward scattering. The reaction thus proceeds, as previously suggested, through a well-defined 'quantized bottleneck state' different from the trapped Feshbach resonance states observed before.