  We use a network of chiral junctions to construct a family of topological
chiral spin liquids in two spatial dimensions. The chiral spin liquid phase
harbors SU(2)$_k$ anyons, which stem from the underlying SU(2)$_k$ WZW models
that describe the constituent spin chains of the network. The network exhibits
quantized spin and thermal Hall conductances. We illustrate our construction by
inspecting the topological properties of the SU(2)$_2$ model. We find that this
model has emergent Ising anyons, with spinons acting as vortex excitations that
bind Majorana zero modes. We also show that the ground state of this network is
threefold degenerate on the torus, asserting its non-Abelian character. Our
results shed new light on the stability of non-Abelian topological phases in
artificial quantum materials.
