High-resolution spectra (range 655-675 nm) are presented of the pre-main sequence triple system UX Tau. Favorable seeing conditions allowed detection of the spectra of the faintest component, where detection of the H-alpha and the Li-I 670.7 nm feature are reported. An estimate of effective temperature, luminosity, and mass leads to the conclusion that the object is a very young, very-low-mass object, close to the mass limit separating stars from brown dwarfs. Lithium abundances and the evolutionary status of the system are discussed, with special attention to the faint companion. A powerful observational test for evolutionary models of very-low-mass stars can come from lithium measurements, which can set restrictions to the maximum internal temperature attained by these objects.