  We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the
kagome lattice. Here we consider the effects of several perturbations: a) a
chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type
term on the bowties of the kagome lattice, and inquire if they can suppport
chiral spin liquids as ground states. The method used to study these
Hamiltonians is a flux attachment transformation that maps the spins on the
lattice to fermions coupled to a Chern-Simons gauge field on the kagome
lattice. This transformation requires us to consistently define a Chern-Simons
term on the kagome lattice. We find that the chirality term leads to a chiral
spin liquid even in the absence of an uniform magnetic field, with an effective
spin Hall conductance of $\sxy = \frac{1}{2}$ in the regime of $XY$ anisotropy.
The Dzyaloshinkii-Moriya term also leads a similar chiral spin liquid but only
when this term is not too strong. An external magnetic field also has the
possibility of giving rise to additional plateaus which also behave like chiral
spin liquids in the $XY$ regime. Finally, we consider the effects of a
ring-exchange term and find that, provided its coupling constant is large
enough, it may trigger a phase transition into a chiral spin liquid by the
spontaneous breaking of time-reversal invariance.
