We present a deepROSATPSPC image of the radio lobes of the nearby galaxy Fornax A (=NGC 1316) and find, after image processing, X‐ray emission closely mimicking the radio emission. We argue that this is the long‐sought inverse Compton radiation produced when cosmic microwave background photons are upscattered off synchrotron emitting electrons in the radio lobes. The derived magnetic field in the lobes is compared with equipartition values and we also discuss the possibility of thermal Bremsstrahlung emission as a souce of lobe X‐rays. This observation constitutes the best case for detection of inverse Compton X‐rays in radio lobes to date. ©1994 American Institute of Physics