First-principles treatments of quantum molecular reaction dynamics have reached the level of quantitative accuracy even in cases with strong non-Born-Oppenheimer effects. This achievement permits the interpretation of puzzling experimental phenomena related to dynamics governed by multiple coupled potential energy surfaces. We present a combined experimental and theoretical study of the photodissociation of formyl radical (HCO). Oscillations observed in the distribution of product states are found to arise from the interference of matter waves-a manifestation analogous to Young's double-slit experiment.