We propose and demonstrate experimentally a novel way of generating sub-10fs deep-UV pulses. The technique is based on chirped-pulse four-wave mixing induced by a broadband near-IR (NIR) pulse and a near-UV pulse. The broadband IR pulse is prepared by preliminarily broadening the spectral width of an NIR pulse by self-phase modulation. The positively chirped broadband IR pulse is suitable for generating a negatively chirped deep-UV pulse, which can be compressed by normal group-velocity dispersion in a transparent medium. Self-compression of the generated deep-UV pulse in air has been demonstrated to produce sub-10fs deep-UV pulses with excellent temporal and spectral profiles for ultrafast spectroscopy in the deep UV.