Context. Trans-Neptunian objects (TNOs) are important bodies, but very little is known about their basic physical properties such as size, density, and albedo. Aims: We intend to determine sizes, albedos, and even densities of a good sample of TNOs, especially those of the largest TNOs because they can be studied the best with different observational techniques. Methods: We took advantage of a stellar occultation by (119951) 2002 KX14 to obtain valuable information by means of high temporal resolution CCD imaging using ULTRACAM at the 4.2 m William Herschel Telescope on La Palma (Spain). Results: Thanks to the high time resolution of ULTRACAM and the large aperture provided by the telescope, we recorded the most accurate chord ever obtained for an occultation by a TNO, with a length of 415 ± 1 km. This is a lower limit to the diameter of (119951) 2002 KX14 assuming that it has a spherical shape. For ellipsoidal objects we developed a method for obtaining equivalent diameters by combining single-chord occultations and accurate astrometry at the time of occultation. By applying this method to (119951) 2002 KX14, we estimate an equal-area equivalent diameter of at least 365+30-21 km. A possible upper limit is 455 ± 27 km, obtained via thermal data. No atmosphere is detected. We obtain a surface temperature higher than 40 K, which precludes the existence of ices, other than water ice, upon the surface, which is consistent with the featureless spectrum of (119951) 2002 KX14. There are no secondary occultation events that could reveal whether there is a ring system, as recently found for the Centaur (10199) Chariklo.