This paper presents the Gödelian Contingency Argument, which extends Gödel's incompleteness theorems into metaphysical arguments for necessary being. By establishing that (1) ontology is the logic of being—an inference to the best explanation for the universe's deep mathematical intelligibility, (2) formal systems capable of arithmetic are inherently contingent, and (3) empirical observation reveals no infinite regresses or violations of fundamental logical laws, we demonstrate that reality requires a necessary, self-grounding foundation. This foundation is identified with the Three Fundamental Laws of Logic (3FLL), which being pre-arithmetic, escape Gödelian limitations. The argument synthesizes insights from the Kalam cosmological and ontological arguments while beginning from mathematically proven premises and incorporating falsifiable empirical claims. By invoking the Principle of Sufficient Reason to reject infinite regress, the argument offers a rigorous path from mathematical logic to metaphysical necessity.