We have performed the first measurement of the coherent ψ(2S) photo-production cross section in ultraperipheral Pb–Pb collisions at the LHC. This charmonium excited state is reconstructed via the ψ(2S) → l +l − and ψ(2S) → J/ψπ+π− decays, where the J/ψ decays into two leptons. The analysis is based on an event sample corresponding to an integrated luminosity of about 22 μb−1. The cross section for coherent ψ(2S) production in the rapidity interval −0.9 < y < 0.9 is dσcoh ψ(2S)/dy = 0.83±0.19 stat+syst mb. The ψ(2S) to J/ψ coherent cross section ratio is 0.34+0.08 −0.07(stat + syst). The obtained results are compared to predictions from theoretical models.