A fundamental issue in classical General Relativity is to determine the amount of energy (gravitational plus matter) contained within a finite domain of spacetime; such a measurement is known as quasi-local mass. One of the most prominent definitions of quasi-local mass was proposed by R. Bartnik, who sought to localize the ADM (or total) mass. This is accomplished by considering all appropriate extensions of a given domain, and taking the infimum of their respective ADM masses. Relying on both geometric and physical intuition, Bartnik conjectured that the infimum is realized by the mass of a solution to the static vacuum Einstein equations satisfying a natural boundary condition. In this talk I will introduce conditions which guarantee the existence of a unique solution to Bartnik's boundary value problem.