  The flat bands resulting from moir\'e superlattices in magic-angle twisted
bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron
nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated
electron phenomena such as correlated insulators and superconductivity. More
recently, orbital magnetism associated with correlated Chern insulators was
found in this class of layered structures centered at integer multiples of n0,
the density corresponding to one electron per moir\'e superlattice unit cell.
Here we report the experimental observation of ferromagnetism at fractional
filling of a flat Chern band in an ABC-TLG/hBN moir\'esuperlattice. The
ferromagnetic state exhibits prominent ferromagnetic hysteresis behavior with
large anomalous Hall resistivity in a broad region of densities, centered in
the valence miniband at n = -2.3 n0. This ferromagnetism depends very
sensitively on the control parameters in the moir\'e system: not only the
magnitude of the anomalous Hall signal, but also the sign of the hysteretic
ferromagnetic response can be modulated by tuning the carrier density and
displacement field. Our discovery of electrically tunable ferromagnetism in a
moir\'e Chern band at non-integer filling highlights the opportunities for
exploring new correlated ferromagnetic states in moir\'e heterostructures.
