An algorithm is described for tagging the flavour content at production of neutral B mesons in the LHCb experiment. The algorithm exploits the correlation of the flavour of a B meson with the charge of a reconstructed secondary charm hadron from the decay of the other b hadron produced in the proton-proton collision. Charm hadron candidates are identified in a number of fully or partially reconstructed Cabibbo-favoured decay modes. The algorithm is calibrated on the self-tagged decay modes B+ → J/ψ K+ and B0 → J/ψ K*0 using 3.0 fb−1 of data collected by the LHCb experiment at pp centre-of-mass energies of 7 TeV and 8 TeV. Its tagging power on these samples of B → J/ψ X decays is (0.30 ± 0.01 ± 0.01)%.