  We construct a two-dimensional (2D) lattice model that is argued to realize a
gapped chiral spin liquid with (Ising) non-Abelian topological order. The
building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin
interactions. The two-leg ladders are then arranged on rows and coupled through
SU(2)-symmetric interactions between consecutive ladders. The intra-ladder
interactions are tuned so as to realize the c = 1/2 Ising conformal field
theory, a fact that we establish numerically via Density Matrix Renormalization
Group (DMRG) studies. Time-reversal breaking inter-ladder interactions are
tuned so as to open a bulk gap in the 2D lattice system. This 2D system
supports gapless chiral edge modes with Ising non-Abelian excitations but no
charge excitations, in contrast to the Pfaffian non-Abelian fractional quantum
Hall state.
