Chile's northern Atacama Desert has been pointed out as one of the places on earth where the world's highest surface ultraviolet (UV) may occur. This area is characterized by its high altitude, prevalent cloudless conditions and relatively low total ozone column. Aimed at detecting those peak UV levels, we carried out in January 2013 ground-based spectral measurements on the Chajnantor Plateau (5100 m altitude, 23°00'S, 67°45'W) and at the Paranal Observatory (2635 m altitude, 24°37'S, 70°24'W). The UV index computed from our spectral measurements peaked at 20 on the Chajnantor Plateau (under broken cloud conditions) and at 16 at the Paranal Observatory (under cloudless conditions). Spectral measurements carried out in June 2005 at the Izaña Observatory (2367 m altitude, 28°18'N, 16°30'W) were used for further comparisons. Due to the differences in sun-earth separation, total ozone column, altitude, albedo, aerosols and clouds, peak UV levels are expected to be significantly higher at southern hemisphere sites than at their northern hemisphere counterparts.