We present observations of the M87 jet made with the Faint Object Camera on board the Hubble Space Telescope at five epochs between 1994 and 1998. These observations reveal 10 superluminal features within the first 6" of the jet, with eight of these having apparent speeds in the range 4c-6c. Two additional features within the first arcsecond of the jet have subluminal speeds of 0.63c and 0.84c. The latter of these, named HST-1 East, appears to emit new superluminal features moving at 6c, which subsequently fade with a half-intensity timescale of ~2 yr. The fastest speeds we observe require a Lorentz factor γ>=6 for the bulk flow and a jet orientation within 19° of the line of sight, in the context of the relativistic jet model. Finding such large γ in an FR I radio source like M87 strongly supports BL Lac/FR I unification models. These large speeds help to mitigate the particle lifetime problem posed by the optical emission, as well as the jet confinement problem.