Research in molecular electronics often involves the demonstration of devices that are analogous to conventional semiconductor devices, such as transistors and diodes(1), but it is also possible to perform experiments that have no parallels in conventional electronics. For example, by applying a mechanical force to a molecule bridged between two electrodes, a device known as a molecular junction, it is possible to exploit the interplay between the electrical and mechanical properties of the molecule to control charge transport through the junction(2-8). 1,4'-Benzenedithiol is the most widely studied molecule in molecular electronics(9-18), and it was shown recently that the molecular orbitals can be gated by an applied electric field(11). Here, we report how the electromechanical properties of a 1,4'-benzenedithiol molecular junction change as the junction is stretched and compressed. Counterintuitively, the conductance increases by more than an order of magnitude during stretching, and then decreases again as the junction is compressed. Based on simultaneously recorded current-voltage and conductance-voltage characteristics, and inelastic electron tunnelling spectroscopy, we attribute this finding to a strain-induced shift of the highest occupied molecular orbital towards the Fermi level of the electrodes, leading to a resonant enhancement of the conductance. These results, which are in agreement with the predictions of theoretical models(14-17,19,20), also clarify the origins of the long-standing discrepancy between the calculated and measured conductance values of 1,4'-benzenedithiol, which often differ by orders of magnitude(21).