We report the results of an X-ray spectral imaging observation of the Antennae with the ROSAT PSPC. 55 per cent of the soft X-ray flux from the system is resolved into discrete sources, including components identified with the galactic nuclei and large Hn regions, whilst the remainder appears to be predominantly genuinely diffuse emission from gas at a temperature similar to 4 x 10(6)K. The morphology of the emission is unusual, combining a halo which envelops the galactic discs with what appears to be a distorted, but well-collimated, bipolar outflow We derive physical parameters for the hot gas in both diffuse components, which are of some interest, given that the Antennae probably represents an elliptical galaxy in the making.