Traditional cosmological arguments are often thought to rely fatally on the Principle of Sufficient Reason. This paper develops a contingency argument that does not. Building on Armstrong’s metaphysics, I propose that no non-empty world is accessible from an empty world. From this it follows that, if only contingent entities exist, the accessibility structure of possible worlds forms either a circularity or an infinite regress. Both are ruled out by a well-foundness principle weaker than Schaffer’s Inheritance of Being. Two possible kinds of non-contingent entities are then distinguished—necessary and isolated entities—and the latter are ruled out by an accessibility principle. The conclusion is that at least one necessary entity must exist.