Carbon nanotubes are chiral molecular objects and therefore exist in two forms that are each other's mirror image. Many aspects of these fascinating new materials have recently been explored but their chirality has hardly been addressed. We have investigated the charge transport through individual single-walled carbon nanotubes in the presence of a magnetic field parallel to the tube axis. For most of the investigated tubes, a dependence of the resistance that is odd in both the magnetic field and in the current through the tube is observed. This effect is ascribed to the chirality of the nanotube and is called electrical magneto-chiral anisotropy.