The combination of chirality and magnetism has steadily grown over the last decennia into an area of intense research. Magnetochiral anisotropy, chirality-induced spin-selectivity and helimagnetism are the most prominent phenomena resulting from this combination, touching different systems like topological (semi-)metals and insulators, quantum magnets, type II multiferroics and enantio-selective synthesis. As an extension to this area, we argue, based on symmetry arguments, that magnetochiral anisotropy will manifest itself in the displacement current in chiral dielectrics in a magnetic field. We confirm this conjecture by the experimental observation of very strong dielectric magnetochiral anisotropy near the ferroelectric phase transitions of triglycine sulfate and Rochelle salt, two of the oldest and most investigated chiral ferroelectrics. This effect opens a new playground in the study and characterisation of all chiral dielectrics. With our discovery, magnetochiral anisotropy now covers the (di)electrical properties of all condensed matter, from insulators to superconductors.