Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD -> H-2 + D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state-resolved differential cross sections in the forward scattering direction for H-2 products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.