  A recent experiment reported a large anomalous Hall effect in Magic Angle
Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN)
substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we
study this system theoretically, and propose explanations of this observation.
We emphasize that the physics for this new system is qualitatively different
from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation
symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting
valence and conduction bands of each valley carry equal and opposite Chern
numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard
model for this system which we derive. An obvious possible explanation of the
anomalous Hall effect is that at $3/4$-filling the system is a spin-valley
polarized ferromagnetic insulator where the electrons completely fill a Chern
band. We also examine an alternate more radical proposal of a compressible
valley polarized but spin unpolarized composite ferm liquid metallic state. We
argue that either state is compatible with current experiments, and propose
ways to distinguish between them in the future. We also briefly discuss the
physics at $1/2$ filling.
