Although the dynamics of collisions between a molecule and a solid surface are ultimately quantum mechanical, decohering effects owing to the large number of interacting degrees of freedom typically obscure the wavelike nature of these events. However, a partial decoupling of internal molecular motion from external degrees of freedom can reveal striking interference effects despite significant momentum exchange between the molecule and the bath of surface vibrations. We report state-prepared and state-resolved measurements of methane scattering from a room-temperature gold surface that demonstrate total destructive interference between molecular states related by a reflection symmetry operation. High-contrast interference effects prevail for all processes investigated, including vibrationally excited and vibrationally inelastic collisions. The results demonstrate the distinctly quantum mechanical effect of discrete symmetries in molecular collision dynamics.