  A Chern--Simons theory for the doped spin-1/2 kagom\'e system is constructed,
from which it is shown that the system is an exotic superconductor that breaks
time-reversal symmetry. It is also shown that the system carries minimal
vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional
superconductors) and contains fractional quasiparticles (including fermionic
quasiparticles with \emph{semionic} mutual statistics and spin-1/2
quasiparticles with \emph{bosonic} self-statistics) in addition to the usual
spin-1/2 fermionic Bougoliubov quasiparticle. Two Chern--Simons theories--one
with an auxiliary gauge field kept and one with the auxiliary field and a
redundant matter field directly eliminated--are presented and shown to be
consistent with each other.
