  We argue that a relatively simple model containing only SU(2)-invariant
chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise
to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in
a formulation in terms of network models of edge states and are backed up by a
careful numerical analysis. For a uniform choice of chirality on the lattice,
we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is
identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a
gapless spin liquid emerges which exhibits gapless spin excitations along lines
in momentum space, a feature that we probe by studying quasi-two-dimensional
systems of finite width. We thus provide a single, appealingly simple spin
model (i) for what is probably the simplest realization of the
Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi liquid state
with lines of gapless SU(2) spin excitations.
