Interest in vortex matter has risen considerably since the discovery of the high-temperature superconductors, which exhibit magnetic vortex states that are especially rich and complex(1). The global behaviour of magnetic vortices in nearly perfect crystals-such as melting of the vortex lattice(2-5)-has been much studied, but of more technological relevance is the influence on the vortex states of the various structural defects present in most practical superconductors. An important example of such a defect is the twin boundary present in twinned orthorhombic crystals of YBa2Cu3O7-delta (YBCO). Studies of such samples using magnetic-field-sensitive probes(6-9) have suggested that the twin boundary plays an important role in pinning the vortices and so enhancing the currents that YBCO can support while remaining superconducting. But the low spatial resolution of these techniques does not permit these effects to be studied at the scale of the vortices or boundaries themselves. Scanning tunnelling spectroscopy offers a means of circumventing these problems of resolution(10-12), as it directly probes the superconducting order parameter at nanometre length scales. Here we use this technique to investigate the importance of twin boundaries in YBCO. In particular we observe an unexpectedly large pinning strength for perpendicular vortex flux across the boundary, which implies that the critical current that can be supported along the boundary approaches the theoretical 'depairing' limit.