  The induced interaction among the majority spin species, due to the presence
of the minority species, is computed for the case of a population-imbalanced
resonantly-interacting Fermi gas. It is shown that this interaction leads to an
instability, at low temperatures, of the recently observed polaron Fermi liquid
phase of strongly imbalanced Fermi gases to a p-wave superfluid state. We find
that the associated transition temperature, while quite small in the weakly
interacting BCS regime, is experimentally accessible in the strongly
interacting unitary regime.
