When neutral molecules with low levels of vibrational excitation collide at metal surfaces, vibrational coupling to electron-hole pairs (EHPs) is not thought to be strong unless incidence energies are high. However, there is accumulating evidence that coupling of large-amplitude molecular vibration to metallic electron degrees of freedom can be much stronger even at the lowest accessible incidence energies. As reaching a chemical transition-state also involves large-amplitude vibrational motion, we pose the basic question: are electronically non-adiabatic couplings important at transition states of reactions at metal surfaces? We have indirect evidence in at least one example that the dynamics and rates of chemical reactions at metal surfaces may be strongly influenced by electronically non-adiabatic coupling. This implies that theoretical approaches relying on the Born-Oppenheimer approximation (BOA) may not accurately reflect the nature of transition-state traversal in reactions of catalytic importance. Developing a predictive understanding of surface reactivity beyond the BOA represents one of the most important challenges to current research in physical chemistry. This article reviews the experimental evidence and underlying theoretical framework concerning these and related topics.