The problem of positive-definiteness of the field energy in general relativity is analyzed and resolved by means of a variational procedure. It is shown that, among all asymptotically flat solutions of the source-free Einstein equations, only flat space extremizes the energy. That the energy is nonnegative is then established by showing that its second variation (i.e., the weak field energy) about this “point” is positive. As a corollary, any solution for which this one number—the total energy—vanishes is everywhere flat. Hence, as in other field theories, the vacuum is the lowest energy state. When usual matter sources (with positive-definite flat-space energy) are minimally coupled to gravitation, the total energy is still positive, and the lowest energy state of the interacting system is again the (combined) vacuum.