The electric απ and magnetic βπ charged pion Compton polarizabilities are of fundamental interest in the low-energy sector of quantum chromodynamics. They are directly linked to the phenomenon of spontaneously broken chiral symmetry within QCD and to the dynamics of the pion-photon interaction. The combination (απ-βπ) was measured at CERN COMPASS via radiative pion Primakoff scattering (Bremsstrahlung of 190 GeV/c π-s) in the nuclear Coulomb field: π + Z → π + γ + Z. The data were corrected for higher-order theoretical effects via a one-pion loop calculation in chiral perturbation theory (ChPT). COMPASS data analysis gives a value απ−βπ = (4.0±1.2stat±1.4syst)×10−4 fm3, in agreement with the ChPT prediction απ−βπ = (5.7±1.0)×10−4 fm3. Previously, pion polarizabilities were studied at different laboratories by pion-photon (Primakoff), photon-nucleon and photon-photon collisions. The COMPASS measurement demonstrates that the charged-pion polarizability is significantly smaller than previous results, roughly by a factor two, with the smallest uncertainties achieved so far. The results are consistent with ChPT predictions, and strengthen the identification of the pion with the Goldstone boson of QCD.