  We propose a procedure for computing the boundary stress tensor associated
with a gravitating system in asymptotically anti-de Sitter space. Our
definition is free of ambiguities encountered by previous attempts, and
correctly reproduces the masses and angular momenta of various spacetimes. Via
the AdS/CFT correspondence, our classical result is interpretable as the
expectation value of the stress tensor in a quantum conformal field theory. We
demonstrate that the conformal anomalies in two and four dimensions are
recovered. The two dimensional stress tensor transforms with a Schwarzian
derivative and the expected central charge. We also find a nonzero ground state
energy for global AdS_5, and show that it exactly matches the Casimir energy of
the dual N=4 super Yang-Mills theory on S^3 x R.
