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Studies of the composition of the fireball produced in very high energy heavy-ion collisions show that the composition is that of an equilibrium gas of hadrons at a temperature of about 155 MeV, and zero chemical potential. At the same time, lattice computations show that the chiral cross over of QCD occurs at a temperature of about 155 MeV. The composition of the fireball is a question of the dynamics of hadron reactions, whereas the location of a cross over is a question about the equilibrium free energy density. I describe a computation which shows why they coincide.