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We obtained deep V (F555W) and I (F814W) images of the central region of the Leo~I dwarf spheroidal (dSph) galaxy using WFPC2 aboard HST. These data reach to I = 26.5 and clearly reveal for the first time the turnoff of the youngest stars in the galaxy. We have used a variety of isochrones to conclude that the bulk of the stellar population of the galaxy is composed of stars as young as 3 Gyr, in excellent agreement with much shallower ground-based observations by Lee et al. (1994, AJ, 106, 1420). Careful analysis of the Leo~I photometry also reveals a significant (10\%) contribution from stars older than 12 Gyr, but little evidence for any star formation between the 3 and 12 Gyr populations . Leo~I has clearly experienced two distinct bursts of star formation, similar to the history of formation in other (most?) dwarf galaxies in the Local Group. We discuss this star formation history in terms of the luminosity and color evolution of Leo~I, with emphasis on the possibility that it may have resembled the so-called faint blue galaxies identified in deep galaxy surveys.