Every star-forming galaxy has a halo of metal-enriched gas that extends out to at least 100 kiloparsecs, as revealed by the absorption lines that this gas imprints on the spectra of background quasars. However, quasars are sparse and typically probe only one narrow beam of emission through the intervening galaxy. Close quasar pairs and gravitationally lensed quasars have been used to circumvent this inherently one-dimensional technique, but these objects are rare and the structure of the circumgalactic medium remains poorly constrained. As a result, our understanding of the physical processes that drive the recycling of baryons across the lifetime of a galaxy is limited. Here we report integral-field (tomographic) spectroscopy of an extended background source—a bright, giant gravitational arc. We can thus coherently map the spatial and kinematic distribution of Mg ɪɪ absorption—a standard tracer of enriched gas—in an intervening galaxy system at redshift 0.98 (around 8 billion years ago). Our gravitational-arc tomography unveils a clumpy medium in which the absorption strength decreases with increasing distance from the galaxy system, in good agreement with results for quasars. Furthermore, we find strong evidence that the gas is not distributed isotropically. Interestingly, we detect little kinematic variation over a projected area of approximately 600 square kiloparsecs, with all line-of-sight velocities confined to within a few tens of kilometres per second of each other. These results suggest that the detected absorption originates from entrained recycled material, rather than in a galactic outflow.