The Solar System Origins Legacy Survey (SSOLS) is a Hubble Space Telescope Treasury Program targeting a very large, well-characterized sample of cold classical Kuiper Belt Objects in an effort to determine the intrinsic properties of the binary systems endemic to that population. Observations for this program were completed in July of 2020, revealing 25 clearly-resolved binary systems and 172 objects currently identified as solitary. Here we will provide an overview of SSOLS, including survey design and motivation, as well as our initial results regarding the intrinsic binary fraction of the cold classical Kuiper Belt. We confirm a very strong trend in apparent binary fraction with system brightness, but also confirm that this can largely be explained as a novel discovery bias. We show that the binary population’s luminosity function is shifted to brighter values with respect to that of solitary objects. The size of this shift can be used to constrain the origin of these binary systems, and the SSOLS preliminary results suggest that this luminosity function shift is approximately 1 magnitude — larger than would be expected through origin scenarios involving common formation through collapse of swarms of cm-scale particles. We will discuss this potential tension with leading theories of the origin of the cold classical KBOs, possible alternative scenarios, and our ongoing efforts to leverage the SSOLS Treasury Sample to illuminate the origin and history of the outer solar system.