We are currently witnessing a new space race, whereby the accessing of outer space resources and the setting up of space colonies are being explored as genuine solutions to the resource problem on Earth. However, the exploration of these endeavors is costly and actors are more likely to secure funding for this pioneering work if they can promise their investors extraterrestrial private property rights. This possibility is currently precluded by article II of the 1967 Outer Space Treaty, which declares that the "[o]uter space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means". In light of the resource problem on Earth, it is debatable whether this complete prohibition should continue to be upheld and how private property - if permitted - can be ethically shared across humanity without endangering peace. This contribution will approach these questions on the basis of Catholic social teaching.