A material is said to exhibit dichroism if its photon absorption spectrum depends on the polarization of the incident radiation. In the case of X-ray magnetic circular dichroism (XMCD), the absorption cross-section of a ferromagnet or a paramagnet in a magnetic field changes when the helicity of a circularly polarized photon is reversed relative to the magnetization direction. Although similarities between X-ray absorption and electron energy-loss spectroscopy in a transmission electron microscope (TEM) have long been recognized, it has been assumed that extending such equivalence to circular dichroism would require the electron beam in the TEM to be spin-polarized. Recently, it was argued on theoretical grounds that this assumption is probably wrong. Here we report the direct experimental detection of magnetic circular dichroism in a TEM. We compare our measurements of electron energy-loss magnetic chiral dichroism (EMCD) with XMCD spectra obtained from the same specimen that, together with theoretical calculations, show that chiral atomic transitions in a specimen are accessible with inelastic electron scattering under particular scattering conditions. This finding could have important consequences for the study of magnetism on the nanometre and subnanometre scales, as EMCD offers the potential for such spatial resolution down to the nanometre scale while providing depth information--in contrast to X-ray methods, which are mainly surface-sensitive.