Chirality can appear at many length scales in nature. In this study the authors introduce planar chirality as a quantitative geometric measure of chirality for two-dimensional objects. They apply this measure to evaluate the chirality of nanometer-sized structures with an electron microscope. They employ an innovative electron-optics device, the orbital-angular-momentum sorter, which applies a log-polar conformal mapping to the electron wave function and reaches near-optimal resolution in orbital angular momentum.