A search for a light charged Higgs boson, originating from the decay of a top quark and subsequently decaying into a charm quark and a strange antiquark, is presented. The data used in the analysis correspond to an integrated luminosity of 19.7 fb$^{−1}$ recorded in proton-proton collisions at $ \sqrt{s}=8 $ TeV by the CMS experiment at the LHC. The search is performed in the process $ \mathrm{t}\overline{\mathrm{t}}\to {\mathrm{W}}^{\pm }{\mathrm{b}\mathrm{H}}^{\mp}\overline{\mathrm{b}} $ , where the W boson decays to a lepton (electron or muon) and a neutrino. The decays lead to a final state comprising an isolated lepton, at least four jets and large missing transverse energy. No significant deviation is observed in the data with respect to the standard model predictions, and model-independent upper limits are set on the branching fraction $ \mathrm{\mathcal{B}}\left(\mathrm{t}\to {\mathrm{H}}^{+}\mathrm{b}\right) $ , ranging from 1.2 to 6.5% for a charged Higgs boson with mass between 90 and 160 GeV, under the assumption that $ \mathrm{\mathcal{B}}\left({\mathrm{H}}^{+}\to \mathrm{c}\mathrm{s}\right)=100% $ .