  We study the effect of electron-electron interactions in a spinful Chern
insulator. For weak on-site repulsive interactions at half-filling, the system
is a weakly correlated Chern insulator adiabatically connected to the
noninteracting ground state, while in the limit of infinitely strong repulsion
the system is described by an effective spin model recently predicted to
exhibit a chiral spin liquid ground state. In the regime of large but finite
repulsion, we find an exotic gapped phase with characteristics partaking of
both the noninteracting Chern insulator and the chiral spin liquid. This phase
has an integer quantized Hall conductivity $2e^2/h$ and quasiparticles with
electric charges that are integer multiples of the electron charge $e$, but the
ground state on the torus is four-fold degenerate and quasiparticles have
fractional statistics. We discuss how these unusual properties affect the
outcome of a charge pumping experiment and, by deriving the topological field
theory, elucidate that the topological order is of the exotic $\mathbb{Z}_2$
double-semion type.
