High-spectral-brightness coherent XUV radiation has been produced by third-harmonic generation of a transformlimited- bandwidth KrF* laser in gaseous xenon. The observed XUV output, which was continuously tunable from 82.8 to 83.3 nm, had a peak power of 40 mW, a bandwidth <0.01 cm(-1), and absolute frequency control to within 0.04 cm(-1). The utility of this XUV source for high-resolution spectroscopic applications is demonstrated by absorption studies in molecular hydrogen.