Ferroelectric materials are heavily used in electro-mechanics and electronics. Inside the ferroelectric, domain walls separate regions in which the spontaneous polarization is differently oriented. Properties of ferroelectric domain walls can differ from those of the domains themselves, leading to new exploitable phenomena. Even more exciting is that a non-ferroelectric material may have domain boundaries that are ferroelectric. Many materials possess translational antiphase boundaries. Such boundaries could be interesting entities to carry information if they were ferroelectric. Here we show first that antiphase boundaries in antiferroelectrics may possess ferroelectricity. We then identify these boundaries in the classical antiferroelectric lead zirconate and evidence their polarity by electronmicroscopy using negative spherical-aberration imaging technique. Ab initio modelling confirms the polar bi-stable nature of the walls. Ferroelectric antiphase boundaries could make high-density non-volatile memory; in comparison with the magnetic domain wall memory, they do not require current for operation and are an order of magnitude thinner.