We present here measurements of the heat capacity at constant pressure near the ceiling temperature for the anionic polymerization of an organic monomer. The measurements support the suggestion [S. J. Kennedy and J. C. Wheeler, J. Chern. Phys. 78, 953 (1983); J. C. Wheeler and P. M. Pfeuty, Phys. Rev. Lett. 71, 1653 (1993)] that the onset of equilibrium polymerization in initiated monomer solutions as the temperature is changed can be viewed as a second-order continuous phase transition. We compare our measurements on living poly(alpha-methylstyrene) initiated by sodium naphthalide in tetrahydrofuran to the theoretical predictions, and find qualitative agreement. We attribute quantitative differences to the dependence of the enthalpy of polymerization on the degree of polymerization and on the tacticity. (C) 1997 American Institute of Physics.