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+ντ . The analysed data correspond to an integrated luminosity of about 2 fb−1 recorded in protonproton collisions at √s = 7 TeV by the CMS experiment at the LHC. The search is sensitive to the decays of the top quark pairs tt¯ → H±W∓ bb¯ and tt¯→ H±H∓ bb¯. 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+ντ) = 1.