  We point out that the zero-energy Landau level of Dirac fermions in graphene
can be, in the presence of a repulsive electron-electron interaction, split
into two (levels) associated with a "bond ordering" formation having a "Kekule
pattern", which respects the chiral symmetry. Since the Kekule pattern has a
three-fold degeneracy, domain structures are implied, for which we show that
in-gap states localized along the domain boundaries exist as topological
states. Based on this a possibility of a quantum-liquid ground state of
graphene in magnetic fields is discussed.
