  Topologically ordered phases are characterized by long-range quantum
entanglement and fractional statistics rather than by symmetry breaking. First
observed in a fractionally filled continuum Landau level, topological order has
since been proposed to arise more generally at fractional filling of
topologically non-trivial "Chern" bands. Here, we report the observation of
gapped states at fractional filling of Harper-Hofstadter bands arising from the
interplay of a magnetic field and a superlattice potential in a bilayer
graphene/hexagonal boron nitride heterostructure. We observe new phases at
fractional filling of bands with Chern indices $\mathcal{C} = -1, \pm 2,$ and
$\pm 3$. Some of these, in $\mathcal{C}=-1$ and $\mathcal{C}=2$ bands, are
characterized by fractional Hall conductance---they are `fractional Chern
insulators' and constitute a new example of topological order beyond Landau
levels.
