  It is shown that in $3+1$ dimensions, a constant magnetic field is a catalyst
of dynamical chiral symmetry breaking, leading to generating a fermion mass
even at the weakest attractive interaction between fermions. The essence of
this effect is the dimensional reduction $D \rightarrow D-2$ ($3+1 \rightarrow
1+1$) in the dynamics of fermion pairing in a magnetic field. The effect is
illustrated in the Nambu-Jona-Lasinio model. Possible applications of this
effect are briefly discussed.
