  We propose that the inversion symmetry of the graphene honeycomb lattice is
spontaneously broken via a magnetic field dependent Peierls distortion. This
leads to valley splitting of the $n=0$ Landau level but not of the other Landau
levels. Compared to quantum Hall valley ferromagnetism recently discussed in
the literature, lattice distortion provides an alternative explanation to all
the currently observed quantum Hall plateaus in graphene.
