  We study the prospects for observing superfluidity in a spin-polarized atomic
gas of $^6$Li atoms, using state-of-the-art interatomic potentials. We
determine the spinodal line and show that a BCS transition to the superfluid
state can indeed occur in the (meta)stable region of the phase diagram if the
densities are sufficiently low. Moreover, for a total density of
$10^{12}~cm^{-3}$, which still fulfills this requirement, we find a critical
temperature of only $29~nK$. We also discuss the stability of the gas due to
exchange and dipolar relaxation and conclude that the prospects for observing
superfluidity in a magnetically trapped atomic $^6$Li gas are particularly
promising for magnetic bias fields larger than $10~T$.
