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We study a frustrated two-dimensional lattice spin model with Kitaev typeinteraction. The lattice is obtained from the honeycomb lattice by replacinghalf of its sites with triangles. Using the SO(3) Majorana representation ofspin, the model is exactly mapped into a $Z_{2}$ lattice gauge theory ofcomplex fermions with standard Gauss law constraint. We show that the groundstate of the model is a chiral spin liquid, and it has gapless excitations. TheChern number of the ground state is $\pm 1$, implying the existence of chiraledge mode. The vortex excitation of the model is bound with a Majorana zeromode, such mode behaves as non-Abelian anyons.

Exact chiral spin liquid state in a Kitaev type spin model