  In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer
tunneling and rotational misalignment conspire to create a pair of low energy
flat band that have been found to host various correlated phenomena at partial
filling. Most work to date has focused on the zero magnetic field phase
diagram, with magnetic field (B) used as a probe of the B=0 band structure.
Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a
cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We
argue that the emergence of the Chern insulators is driven by the interplay of
the moire superlattice with the B, which endow the flat bands with a
substructure of topologically nontrivial subbands characteristic of the
Hofstadter butterfly. The new phases can be accounted for in a Stoner picture
in which exchange interactions favor polarization into one or more spin- and
valley-isospin flavors; in contrast to conventional quantum Hall ferromagnets,
however, electrons polarize into between one and four copies of a single
Hofstadter subband with Chern number C=-1. In the case of the C=\pm3 insulators
in particular, B catalyzes a first order phase transition from the spin- and
valley-unpolarized B=0 state into the ferromagnetic state. Distinct from other
moire heterostructures, tBLG realizes the strong-lattice limit of the
Hofstadter problem and hosts Coulomb interactions that are comparable to the
full bandwidth W and are consequently much stronger than the width of the
individual Hofstadter subbands. In our experimental data, the dominance of
Coulomb interactions manifests through the appearance of Chern insulating
states with spontaneously broken superlattice symmetry at half filling of a
C=-2 subband. Our experiments show that that tBLG may be an ideal venue to
explore the strong interaction limit within partially filled Hofstadter bands.
