Glasses are rigid, but flow when the temperature is increased. Similarly, granular materials are rigid, but become unjammed and flow if sufficient shear stress is applied. The rigid and flowing phases are strikingly different, yet measurements reveal that the structures of glass and liquid are virtually indistinguishable. It is therefore natural to ask whether there is a structural signature of the jammed granular state that distinguishes it from its flowing counterpart. Here we find evidence for such a signature, by measuring the contact-force distribution between particles during shearing. Because the forces are sensitive to minute variations in particle position, the distribution of forces can serve as a microscope with which to observe correlations in the positions of nearest neighbours. We find a qualitative change in the force distribution at the onset of jamming. If, as has been proposed, the jamming and glass transitions are related, our observation of a structural signature associated with jamming hints at the existence of a similar structural difference at the glass transition--presumably too subtle for conventional scattering techniques to uncover. Our measurements also provide a determination of a granular temperature that is the counterpart in granular systems to the glass-transition temperature in liquids.