We report the first experimental observation of the depolarization of the Thomson scattering (TS) radiation, a relativistic effect expected to occur in very high T-e plasmas and never observed so far in a fusion machine. A set of unused optical fibers in the collection optics of the high resolution Thomson scattering system of JET has been used to detect the depolarized TS radiation during a JET campaign with T-e <= 8 keV. A linear polarizer with the axis perpendicular to the direction of the incident E-field was placed in front of a fiber optic pair observing a region close to the plasma core, while another fiber pair with no polariser simultaneously observed an adjacent plasma region. The measured intensity ratio was found to be consistent with the theory, taking into account sensitivity coefficients of the two measurement channels determined with post-experiment calibrations and Raman scattering. This depolarization effect is at the basis of polarimetric TS, a different and complementary method for the analysis of TS spectra that can provide significant advantages for T-e measurements in very hot plasmas such as in ITER (T-e <= 40 keV).