  We calculate the electron self-energy in a magnetized QED plasma to the
leading perturbative order in the coupling constant and to the linear order in
an external magnetic field. We find that the chiral asymmetry of the normal
ground state of the system is characterized by two new Dirac structures. One of
them is the familiar chiral shift previously discussed in the
Nambu--Jona-Lasinio model. The other structure is new. It formally looks like
that of the chiral chemical potential but is an odd function of the
longitudinal component of the momentum, directed along the magnetic field. The
origin of this new parity-even chiral structure is directly connected with the
long-range character of the QED interaction. The form of the Fermi surface in
the weak magnetic field is determined.
