  We show that a honeycomb lattice of Heisenberg spin-$1/2$ chains with
three-spin junction interactions allows for controlled analytical studies of
chiral spin liquids (CSLs). Tuning these interactions to a chiral fixed point,
we find a Kalmeyer-Laughlin CSL phase which here is connected to the critical
point of a boundary conformal field theory. Our construction directly yields a
quantized spin Hall conductance and localized spinons with semionic statistics
as elementary excitations. We also outline the phase diagram away from the
chiral point where spinons may condense. Generalizations of our approach can
provide microscopic realizations for many other CSLs.
