Interferences are genuine quantum phenomena that appear whenever two seemingly distinct classical trajectories lead to the same outcome. They are common in elastic scattering but are seldom observable in chemical reactions. Here we report experimental measurements of the state-to-state angular distribution for the H + D 2 reaction using the ' photoloc' technique. For products in low rotational and vibrational states, a characteristic oscillation pattern governs backward scattering. The comparison between the experiments, rigorous quantum calculations and classical trajectories on an accurate potential energy surface allows us to trace the origin of that structure to the quantum interference between different quasiclassical mechanisms, a phenomenon analogous to that observed in the double-slit experiment.