  In this letter, we examine the role of Coulomb interactions in the emergence
of macroscopically ordered states in graphene supported on hexagonal boron
nitride substrates. Due to incommensuration effects with the substrate,
graphene can develop gapped low energy modes that spatially conform into a
triangular superlattice of quantum rings. In the presence of these modes, we
show that Coulomb interactions lead to spontaneous formation of chiral loop
currents in bulk and to macroscopic spin-valley order at zero temperature. We
show that this exotic state breaks time reversal symmetry and can be detected
with interferometry and polar Kerr measurements.
