The production of prompt Ds+ mesons was measured for the first time in collisions of heavy nuclei with the ALICE detector at the LHC. The analysis was performed on a data sample of Pb-Pb collisions at a centre-of-mass energy per nucleon pair, (Formula presented.) , of 2.76 TeV in two different centrality classes, namely 0–10% and 20–50%. Ds+ mesons and their antiparticles were reconstructed at mid-rapidity from their hadronic decay channel Ds+ → ϕπ+, with ϕ → K−K+, in the transverse momentum intervals 4 < pT < 12GeV/c and 6 < pT < 12 GeV/c for the 0–10% and 20–50% centrality classes, respectively. The nuclear modification factor RAA was computed by comparing the pT-differential production yields in Pb-Pb collisions to those in proton-proton (pp) collisions at the same energy. This pp reference was obtained using the cross section measured at (Formula presented.) TeV and scaled to (Formula presented.) TeV. The RAA of Ds+ mesons was compared to that of non-strange D mesons in the 10% most central Pb-Pb collisions. At high pT (8 < pT < 12 GeV/c) a suppression of the Ds+-meson yield by a factor of about three, compatible within uncertainties with that of non-strange D mesons, is observed. At lower pT (4 < pT < 8 GeV/c) the values of the Ds+-meson RAA are larger than those of non-strange D mesons, although compatible within uncertainties. The production ratios Ds+/D0 and Ds+/D+ were also measured in Pb-Pb collisions and compared to their values in proton-proton collisions.