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The first measurement of the polarisation of coherently photoproduced J∕𝜓 mesons in ultra-peripheral Pb–Pb collisions, using data at √𝑠NN = 5.02 TeV, is presented. The J∕𝜓 meson is measured via its dimuon decay channel in the forward rapidity interval −4.0 <𝑦< −2.5 using the ALICE detector at the CERN LHC. An event sample corresponding to an integrated luminosity of 750 𝜇b−1 ± 5% (syst) is analysed. Hadronic activity is highly suppressed since the interaction is mediated by a photon. The polar and azimuthal angle distributions of the decay muons are measured, and the polarisation parameters 𝜆𝜃, 𝜆𝜑, 𝜆𝜃𝜑 are extracted. The analysis is carried out in the helicity frame. The results are found to be consistent with a transversely polarised J∕𝜓. These values are compared with previous measurements by the H1 and ZEUS experiments. The polarisation parameters of coherent J∕𝜓 photoproduction in Pb–Pb collisions are found to be consistent with the 𝑠-channel helicity conservation hypothesis.