Generation of sub-20-fs UV pulses with more than 300 μJ energy at 268 nm is reported. First, the UV pulses are produced by successive second-harmonic and third-harmonic (TH) generation of 805 nm pulses of a 1 kHz Ti:sapphire laser amplifier. The spectral broadening of TH pulses is realized in a filament, generated in argon. The produced pulses are compressed in a simple double-pass prism-pair compressor. Starting from 100 fs pulses, we achieve a fivefold pulse shortening.