  We theoretically investigate, within the Schwinger-Boson mean-field theory,
the transition from a gapped $Z_{2}$ quantum spin-liquid, in a $J_1$-$J_2$
Heisenberg spin-1/2 system in a honeycomb lattice, to a chiral $Z_2$ spin
liquid phase under the presence of time-reversal symmetry breaking scalar
chiral interaction (with amplitude $J_{\chi}$), with non-trivial Chern bands of
the excitations. We numerically obtain a phase diagram of such
$J_1$-$J_2$-$J_{\chi}$ system, where different phases are distinguished based
on the gap and the nature of excitation spectrum, topological invariant of the
excitations, the nature of spin-spin correlation and the symmetries of the
mean-field parameters. The chiral $Z_2$ state is characterized by non-trivial
Chern number of the excitation bands and lack of long-range magnetic order,
which leads to large thermal Hall coefficient.
