  We show that the decorated honeycomb lattice supports a number of topological
insulating phases with a non-trivial Z_2 invariant and time-reversal symmetry
protected gapless edge modes. We investigate the stability of these phases with
respect to various symmetry breaking perturbations and demonstrate the
connection to the recently discovered exactly solvable S=1/2 chiral spin liquid
model [Phys. Rev. Lett. 99, 247203 (2007)] with non-Abelian and Abelian
excitations on the same lattice. Our work highlights the relationship between
topological band insulators and topologically ordered spin systems, and points
to promising avenues for enlarging the number of known examples of both.
