To whom does outer space ‘belong’? This question lead to space law’s first treaty provision and its most fundamental disputes, but remains unanswered. This ambiguity empowers the loudest interpreters to conquer the cosmos in plain sight – a conquest that continues today in how we read its law, how we remember its past, and how we imagine its future. Space can only be as common as its history. This counterhistory of the decade from Sputnik to the Outer Space Treaty expands our discipline’s origin story. Through reviving these histories, we can see the space commons which might have been, and reimagine the scope of our law’s potential.