Conclusive evidence is presented for the existence of a reactive resonance in the F+HD reaction. In a molecular beam experiment, the resonance appears in the integral cross section as a distinct steplike feature, while in the differential cross section it is manifested as sharply varying forward-backward peaks in the product distribution. A detailed analysis of the quantum dynamics establishes that a reactive resonance localized in the transition-state region is responsible for these remarkable observations. At collision energies below 1 kcal/mol, the reaction proceeds almost exclusively through resonant tunneling with very little contribution from the more conventional direct mechanism.