We use an all-optical trap to confine a strongly attractive two-state mixtu
re of lithium fermions. By measuring the rate of evaporation from the trap,
we determine the effective elastic scattering cross section 4 pi a(2) to s
how that the magnitude of the scattering length /a/ is very large, in agree
ment with predictions. We show that the mixture is stable against inelastic
decay provided that a small bias magnetic field is applied. For this syste
m, the s-wave interaction is widely tunable at low magnetic field, and can
be turned on and off rapidly via a Raman pi pulse. Hence, this mixture is w
ell suited for fundamental studies of an interacting Fermi gas.