On 28th January 2018, the large Trans-Neptunian Object 2002 TC_302_ occulted a m_v_~15.3 star with designation 593-005847 in the UCAC4 stellar catalog, corresponding to Gaia source 130957813463146112. Twelve positive occultation chords were obtained from Italy, France, Slovenia and Switzerland. Also, four negative detections were obtained near the north and south limbs. This represents the best observed stellar occultation by a TNO other than Pluto in terms of the number of chords published thus far. From the twelve chords, an accurate elliptical fit to the instantaneous projection of the body can be obtained, compatible with the near misses. The resulting ellipse has major and minor axes of 543+/-18km and 460+/-11km, respectively, with a position angle of 3+/-1 degrees for the minor axis. This information, combined with rotational light curves obtained with the 1.5-m telescope at Sierra Nevada Observatory and the 1.23-m telescope at Calar Alto observatory, allows us to derive possible three-dimensional shapes and density estimations for the body based on hydrostatic equilibrium assumptions. The effective diameter in equivalent area is around 84km smaller than the radiometrically derived diameter using thermal data from Herschel and Spitzer Space Telescopes. This might indicate the existence of an unresolved satellite of up to ~300km in diameter, to account for all the thermal flux, although the occultation and thermal diameters are compatible within their error bars given the considerable uncertainty of the thermal results. The existence of a potential satellite also appears to be consistent with other ground-based data presented here. From the effective occultation diameter combined with absolute magnitude measurements we derive a geometric albedo of 0.147+/-0.005, which would be somewhat smaller if 2002 TC_302_ has a satellite. The best occultation light curves do not show any signs of ring features or any signatures of a global atmosphere.