  The Fractional Quantum Hall (FQH) effect has been predicted to occur in
absence of magnetic fields and at high temperature in lattice systems that have
flat bands with non-zero Chern number. We demonstrate that the presence of
orbital degrees of freedom in frustrated lattice systems leads to a narrowing
of topologically nontrivial bands. This robust effect does not rely on a
fine-tuning of long-range hopping parameters as do other recent proposals to
realize lattice FQH states and is directly relevant to a wide class of
transition metal compounds.
