We investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in quenched SU(2) gauge theory on the lattice. In agreement with the predictions of the chiral perturbation theory, the chiral condensate grows linearly with the field strength up to (e B)^(1/2) = 1.5 GeV. In the background magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger Hausdorf dimensionality. This delocalization increases the degeneracy of near-zero eigenmodes, and, according to the Banks-Casher relation, enhances the chiral symmetry breaking.