The size distribution in the Kuiper Belt records physical processes operating during the formation and subsequent evolution of the solar system. This paper reports a study of the apparent magnitude distribution of faint objects in the Kuiper Belt, obtained via deep imaging on the Canada-France-Hawaii Telescope and the ESO Very Large Telescope UT1. We find that the entire range of observed objects (magnitudes mR~20-27) is well represented by an unbroken power law, with the number of objects per square degree brighter than magnitude R being of the form Σ(mR<R)=10α(R-R0), with α=0.69 and R0=23.5. This luminosity function's slope implies a steep size distribution in the observed range, which should ``roll over'' to a shallower ``collisional'' slope once observations extend to even fainter magnitudes and thus sample bodies whose collisional ages become less than the age of the solar system. Our observations indicate the roll over is for diameters of less than 50 km, in agreement with collisional models. Modeling our survey gives a belt mass between 30 and 50 AU of order 0.1 M⊕, relatively insensitive to the roll over diameter as long as the latter is >~1 km. We report the discovery of several objects outside of 48 AU and discuss the evidence for a sharp outer edge to the trans-Neptunian distribution.