This paper proposes a well-defined procedure for computing the boundary stress tensor of a gravitating system in asymptotically anti-de Sitter (AdS) space. The method avoids ambiguities found in previous approaches and correctly reproduces the masses and angular momenta of various spacetimes. Through the AdS/CFT correspondence, the classical result is interpreted as the expectation value of the stress tensor in a quantum conformal field theory (CFT). The conformal anomalies in two and four dimensions are recovered, and the two-dimensional stress tensor transforms with a Schwarzsian derivative and the expected central charge. A nonzero ground state energy is found for global AdS₅, matching the Casimir energy of the dual N=4 super Yang-Mills theory on S³×R. The paper introduces a new procedure for defining the stress tensor of asymptotically locally anti-de Sitter spacetimes by renormalizing the stress-energy of gravity with a finite series in boundary curvature invariants. The required terms are uniquely determined by ensuring the stress tensor is finite. The stress tensor is shown to correctly reproduce the masses and angular momenta of various asymptotically AdS spacetimes. For AdS₃, the stress tensor transforms under diffeomorphisms as a tensor plus a Schwarzian derivative, leading to a Virasoro algebra with central charge c = 3ℓ/2G, consistent with Brown and Henneaux's result. The stress tensor also exhibits the correct trace anomaly T_μ^μ = -c/(24π)R. For AdS₄, the stress tensor is shown to have a traceless structure, consistent with the AdS/CFT correspondence. For AdS₅, the stress tensor is found to have a trace anomaly consistent with the conformal anomaly of N=4 super Yang-Mills. The paper also discusses the Casimir energy of the dual N=4 super Yang-Mills theory on S³×R, showing that it matches the gravitational mass of global AdS₅. The paper concludes by discussing the prospects for defining an analogous quasilocal stress tensor in asymptotically flat spacetimes.This paper proposes a well-defined procedure for computing the boundary stress tensor of a gravitating system in asymptotically anti-de Sitter (AdS) space. The method avoids ambiguities found in previous approaches and correctly reproduces the masses and angular momenta of various spacetimes. Through the AdS/CFT correspondence, the classical result is interpreted as the expectation value of the stress tensor in a quantum conformal field theory (CFT). The conformal anomalies in two and four dimensions are recovered, and the two-dimensional stress tensor transforms with a Schwarzsian derivative and the expected central charge. A nonzero ground state energy is found for global AdS₅, matching the Casimir energy of the dual N=4 super Yang-Mills theory on S³×R. The paper introduces a new procedure for defining the stress tensor of asymptotically locally anti-de Sitter spacetimes by renormalizing the stress-energy of gravity with a finite series in boundary curvature invariants. The required terms are uniquely determined by ensuring the stress tensor is finite. The stress tensor is shown to correctly reproduce the masses and angular momenta of various asymptotically AdS spacetimes. For AdS₃, the stress tensor transforms under diffeomorphisms as a tensor plus a Schwarzian derivative, leading to a Virasoro algebra with central charge c = 3ℓ/2G, consistent with Brown and Henneaux's result. The stress tensor also exhibits the correct trace anomaly T_μ^μ = -c/(24π)R. For AdS₄, the stress tensor is shown to have a traceless structure, consistent with the AdS/CFT correspondence. For AdS₅, the stress tensor is found to have a trace anomaly consistent with the conformal anomaly of N=4 super Yang-Mills. The paper also discusses the Casimir energy of the dual N=4 super Yang-Mills theory on S³×R, showing that it matches the gravitational mass of global AdS₅. The paper concludes by discussing the prospects for defining an analogous quasilocal stress tensor in asymptotically flat spacetimes.