  At partial filling of a flat band, strong electronic interactions may favor
gapped states harboring emergent topology with quantized Hall conductivity.
Emergent topological states have been found in partially filled Landau levels
and Hofstadter bands; in both cases, a large magnetic field is required to
engineer the underlying flat band. The recent observation of quantum anomalous
Hall effects (QAH) in narrow band moir\'e systems has led to the theoretical
prediction that such phases may be realized even at zero magnetic field. Here
we report the experimental observation of insulators with Chern number $C=1$ in
the zero magnetic field limit at $\nu=3/2$ and $7/2$ filling of the moir\'e
superlattice unit cell in twisted monolayer-bilayer graphene (tMBG). Our
observation of Chern insulators at half-integer values of $\nu$ suggests
spontaneous doubling of the superlattice unit cell, in addition to spin- and
valley-ferromagnetism. This is confirmed by Hartree-Fock calculations, which
find a topological charge density wave ground state at half filling of the
underlying $C=2$ band, in which the Berry curvature is evenly partitioned
between occupied and unoccupied states. We find the translation symmetry
breaking order parameter is evenly distributed across the entire folded
superlattice Brillouin zone, suggesting that the system is in the flat band,
strongly correlated limit. Our findings show that the interplay of quantum
geometry and Coulomb interactions in moir\'e bands allows for topological
phases at fractional superlattice filling that spontaneously break
time-reversal symmetry, a prerequisite in pursuit of zero magnetic field phases
harboring fractional statistics as elementary excitations or bound to lattice
dislocations.
