We theoretically investigate, within Schwinger-boson mean-field theory, the transition from a gapped ${\mathbb{Z}}_{2}$ quantum spin liquid, in a ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg spin-$\frac{1}{2}$ system in a honeycomb lattice, to a chiral ${\mathbb{Z}}_{2}$ spin-liquid phase under the presence of time-reversal symmetry-breaking scalar chiral interaction (with amplitude ${J}_{\ensuremath{\chi}}$). We numerically obtain a phase diagram of this ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{\ensuremath{\chi}}$ system, where different ground states 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 ${\mathbb{Z}}_{2}$ state is characterized by the nontrivial Chern number of the excitation bands and lack of long-range magnetic order, which leads to a large thermal Hall coefficient.