  We show that the chiral-symmetry-broken phase of massless QED in the presence
of a magnetic field exhibits strong paraelectricity. A large anisotropic
electric susceptibility develops in the infrared region, where most of the
fermions are confined to their lowest Landau level, and dynamical mass and
anomalous magnetic moment are generated via the magnetic catalysis mechanism.
The nonperturbative nature of this effect is reflected in the dependence of the
electric susceptibility on the fine-structure constant. The strong
paraelectricity is linked to the electric dipole moments of the
particle/anti-particle pairs that form the chiral condensate. The significant
electric susceptibility can be used as a probe to detect the realization of the
magnetic catalysis of chiral symmetry breaking in physical systems.
