A fast-growing global space economy requires a clear, consistent, and transparent regime of rights and remedies that can balance the needs and interests of private and State actors. The opposite – politicization of rights and an absence of the rule of law – breeds uncertainty, hinders the peaceful and effective settlement of disputes, and impedes private investment flows in outer space. Within the context of State responsibility, the scope and nature of private rights and remedies are guided by three main questions. First, should States protect private actors and their investments in outer space? Second, which rights should be protected in outer space? Third, how might private actors exercise such rights to seek redress for harm committed by States in outer space? Insights and lessons from the international investment law regime are well-suited to assist in the strengthening of an international rules-based space order.