Magnetic circular dichroism (MCD) is a standard technique for the study of magnetic properties of materials in synchrotron beamlines. We present here a scattering geometry in the transmission electron microscope through which MCD can be observed with unprecedented spatial resolution. A convergent electron beam is used to scan a cross sectional preparation of a Fe/Au multilayer sample. Differences in the energy-loss spectra induced by the magnetic moments of the Fe atoms can be resolved with a resolution of better than 2 nm. This is a breakthrough achievement when compared both to the previous energy-loss MCD resolution (200 nm) or the best x-ray MCD experiments (approximately 20 nm).