We construct net baryon number and strangeness susceptibilities as well as correlations between electric charge, strangeness and baryon number from experimental data at midrapidity of the ALICE Collaboration at CERN. The data were taken in central Pb–Pb collisions at sNN=2.76 TeV and cover one unit of rapidity. The resulting fluctuations and correlations are consistent with Lattice QCD results at the chiral crossover pseudocritical temperature Tc≃155 MeV. This agreement lends strong support to the assumption that the fireball created in these collisions is of thermal origin and exhibits characteristic properties expected in QCD at the transition from the quark gluon plasma to the hadronic phase. The volume of the fireball for one unit of rapidity at Tc is found to exceed 3000 fm3. A detailed discussion on uncertainties in the temperature and volume of the fireball is presented. The results are linked to pion interferometry measurements and predictions from percolation theory.