Circular dichroism spectroscopy is an essential technique for understanding molecular structure and magnetic materials, but spatial resolution is limited by the wavelength of light, and sensitivity sufficient for single-molecule spectroscopy is challenging. We demonstrate that electrons can efficiently measure the interaction between circularly polarized light and chiral materials with deeply sub-wavelength resolution. By scanning a nanometer-sized focused electron beam across an optically-excited chiral nanostructure and measuring the electron energy spectrum at each probe position, we produce a high-spatial-resolution map of near-field dichroism. This technique offers a nanoscale view of a fundamental symmetry and could be employed as photon staining to increase biomolecular material contrast in electron microscopy.