The ALICE Collaboration at the LHC has measured the J/ψ and ψ′ photoproduction at mid-rapidity in ultra-peripheral Pb–Pb collisions at √sNN=2.76 TeV. The charmonium is identified via its leptonic decay for events where the hadronic activity is required to be minimal. The analysis is based on an event sample corresponding to an integrated luminosity of about 23 μb−1. The cross section for coherent and incoherent J/ψ production in the rapidity interval −0.9