  Recent experiment has shown that the ABC-stacked trilayer graphene-boron
nitride Moire super-lattice at half-filling is a Mott insulator. Based on
symmetry analysis and effective band structure calculation, we propose a
valley-contrasting chiral tight-binding model with local Coulomb interaction to
describe this Moire super-lattice system. By matching the positions of van Hove
points in the low-energy effective bands, the valley-contrasting staggered flux
per triangle is determined around $\pi /2$. When the valence band is
half-filled, the Fermi surfaces are found to be perfectly nested between the
two valleys. Such an effect can induce an inter-valley spiral order with a gap
in the charge excitations, indicating that the Mott insulating behavior
observed in the trilayer graphene-boron nitride Moire super-lattice results
predominantly from the inter-valley scattering.
