Microflares are frequent, short-duration, energetically weak disturbances occurring in the nonradiatively heated regions of the Sun and other magnetically active stars. They are thought to be the low-energy extension of flares commonly seen on active dMe stars and may be a major source of heating the chromosphere and corona of cool stars in general. In this paper we describe rapid time sequence UV photometry of the dMe star CN Leo taken with the High Speed Photometer (HSP) aboard the Hubble Space Telescope (HST). The filter was centered at 240 nm, near wavelengths at which flares are expected to have maximum intensity and the stellar background is small. During 2 hr of on-source observing, a total of 32 flarelike events were detected, with integrated counts ranging from 12 to more than 14,000. In most cases the events had integrated energy ranging between 1027 and 1028 ergs and can be classified as microflares. A considerable fine structure was seen in these events, with substantial variations sometimes occurring on timescales of less than 1 s. The occurrence rates for the smaller events showed a power-law distribution, with a slope comparable to that seen for larger events observed from the ground. Extrapolating the occurrence rate relation to nanoflare energies indicates a predicted count rate that is significantly smaller than that observed, suggesting that the nanoflares have a different energy distribution than the larger events.