A bstract Results are presented on a search for a light charged Higgs boson that can be produced in the decay of the top quark t → H + b and which, in turn, decays into τ + ν τ . The analysed data correspond to an integrated luminosity of about 2 fb −1 recorded in protonproton collisions at $ \sqrt {s} = 7\;TeV $ by the CMS experiment at the LHC. The search is sensitive to the decays of the top quark pairs $ {\text{t}}\overline {\text{t}} $ → H ± W ∓ $ {\text{b}}\overline {\text{b}} $ and $ {\text{t}}\overline {\text{t}} $ → H ± H ∓ $ {\text{b}}\overline {\text{b}} $ . Various final states have been studied separately, all requiring presence of a τ lepton from H + decays, missing transverse energy, and multiple jets. Upper limits on the branching fraction B (t → H + b) in the range of 2-4 % are established for charged Higgs boson masses between 80 and 160 GeV, under the assumption that B (H + → τ + ν τ ) = 1.