  We investigate pairing instabilities in the Fermi-liquid-like state of a
single species of anyons. We describe the anyons as Fermions interacting with a
Chern-Simons gauge field and consider the weak coupling limit where their
statistics approaches that of Fermions. We show that, within the conventional
BCS approach, due to induced repulsive Coulomb and current-current
interactions, the attractive Aharonov-Bohm interaction is not sufficient to
generate a gap in the Fermion spectrum.
