  It is shown that the chiral symmetry is spontaneously broken by a constant
magnetic field in QED. The dynamical mass of fermions (energy gap in the
fermion spectrum) is $m_{dyn}\simeq
C\sqrt{eB}\exp\left[-\left(\pi/\alpha\right) ^{1/2}\right]$, where $B$ is the
magnetic field, the constant $C$ is of order one and $\alpha=e^2/4\pi$ is the
renormalized coupling constant. Possible applications of this effect are
discussed.
