The disk of the Milky Way contains free electrons and magnetic fields which contribute significantly to the energetics of the interstellar medium(1). The concentrations of electrons and magnetic fields are too low to be detected by direct methods, but may be investigated using Faraday rotation, a wavelength-dependent shift in linear polarization angle induced by a magneto-ionic medium(2). Structures in polarization angle arising from Faraday rotation have been detected recently at lone, radio wavelengths(3). These structures are disorganized and filamentary, probably arising from interstellar gas in the vicinity of the Sun. Here we report a more distant, highly ordered Faraday-rotation structure of elliptical shape, with its long axis parallel to the plane of the Galaxy The feature appears to be located in an inter-arm region of the Milky Way, between the spiral arm containing the Sun and the next outer (Perseus) spiral arm. Within the elliptical region, small-scale structure which characterizes the turbulence seen in adjacent regions of the interstellar medium is absent. The origin of this magneto-ionic feature is uncertain, but it must arise from an organization of the magnetic-held and electron-density distributions on a scale of the order of 50 parsecs (165 light years).