  We consider a Fermi gas with two components of different masses, with the
s-wave two-body interaction tuned to unitarity. In the range of mass ratio
8.62<M/m<13.6, it is possible for a single contact interaction between heavy
fermions to produce a resonance in a three-body channel. The resulting system
is scale invariant and has universal properties, and is very strongly
interacting. When M/m is slightly above the lower limit 8.62, the ground state
energy of a 2:1 mixture of heavy and light fermions is less than 2% of the
energy of a noninteracting gas with the same number densities. We derive exact
relationships between the pressures of the unitary Fermi gases with and without
three-body resonance when the mass ratio is close to the critical values of
8.62 and 13.6. Possible experimental realization with cold atoms in optical
lattices is discussed.
