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Daily monitoring of PKS 2155−304 with the IUE satellite throughout November 1991 has revealed dramatic, large-amplitude, rapid variations in the ultraviolet flux of this BL Lac object. Many smaller, rapid flares are superimposed on a general doubling of the intensity. During the five-day period when sampling was roughly continuous, the rapid flaring had an apparent quasi-periodic nature, with peaks repeating every ∼ 0.7 days. The short-and long-wavelength ultraviolet light curves are well correlated with each other, and with the optical light curve deduced from the Fine Error Sensor (FES) on IUE. The formal lag is zero but the cross-correlation is asymmetric in the sense that the shorter wavelength emission leads the longer. The ultraviolet spectral shape varies a small but significant amount. The correlation between spectral shape and intensity is complicated; an increase in intensity is associated with spectral hardening, but lags behind the spectral change by ∼ 1 day. The sign of the correlation is consistent with the nonthermal acceleration processes expected in relativistic plasmas, so that the present results are consistent with relativistic jet models, which can also account for quasi-periodic flaring. In contrast, currently proposed accretion disk models are strongly ruled out by the simultaneous optical and ultraviolet variability.