We report the first demonstration of broadband VUV light generation through cascaded nonlinear wave mixing in a gas. Using a hollow-fiber geometry to achieve broad-bandwidth phase-matching, frequency conversion of ultrashort-pulse Ti:sapphire laser pulses from the visible into the deep UV around 200 and 160 nm is achieved. A new type of quasi-phase-matching is also observed in the VUV for the first time. Conversion using cascaded processes exhibits higher efficiencies, shorter pulse durations, and broader bandwidths than other schemes for generating light in the deep UV, and will enable many applications in science and technology.