  We study two models for spinless fermions featuring topologically non-trivial
bands characterized by Chern numbers $C=\pm1$ at fractional filling. Using
exact diagonalization, we show that, even for infinitely strong
nearest-neighbor repulsion, the ground states of these models belong to the
recently discovered class of quantum liquids called fractional Chern insulators
(FCI). We thus establish that FCI states can arise even if interaction
strengths are arbitrarily larger than the noninteracting band gap, going beyond
the limits in which FCI states have been previously studied. The
strong-coupling FCI states therefore depart from the usual isolated-band
picture that parallels the fractional quantum Hall effect in Landau levels and
demonstrate how a topologically ordered state can arise in a truly multiband
system.
