We investigate the constraints that Olbers Paradox, applied to the Zodiacal Background as measured from space, sets on outer solar system objects. If extended to very faint limits, R = 40--50 mag, the steep optical luminosity function (LF) of Kuiper Belt objects (KBOs) at R less than 26 mag implies an infinitely bright night sky. Small KBOs with radii of 1 mm to 1 km must have a size distribution n(r) proportional to r^{-a}, with a = 3.5 or smaller to satisfy the known limits on the sky-surface brightness at optical and far-infrared wavelengths. Improved limits on the measured KBO surface brightness can yield direct estimates of the albedo, temperature, and size distribution for small KBOs in the outer solar system.

4 pages and 2 figures; submitted to Astrophysical Journal Letters