  We extend the Yao-Kivelson decorated honeycomb lattice Kitaev model [Phys.
Rev. Lett. 99,247203 (2007)] of an exactly solvable chiral spin liquid by
including disordered exchange couplings. We have determined the phase diagram
of this system and found that disorder enlarges the region of the topological
non-Abelian phase with finite Chern number. We study the energy level
statistics as a function of disorder and other parameters in the Hamiltonian,
and show that the phase transition between the non-Abelian and Abelian phases
of the model at large disorder can be associated with pair annihilation of
extended states at zero energy. Analogies to integer quantum Hall systems,
topological Anderson insulators, and disordered topological Chern insulators
are discussed.
