  We compute the energy of 2+1 Minkowski space from a covariant action
principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic
flatness, we first show that the 2+1 Einstein-Hilbert action with
Gibbons-Hawking boundary term is both finite on-shell (apart from past and
future boundary terms) and stationary about solutions under arbitrary smooth
asymptotically flat variations of the metric. Thus, this action provides a
valid variational principle and no further boundary terms are required. We then
obtain the gravitational Hamiltonian by direct computation from this action.
The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an
overall addititve constant. This constant is such that 2+1 Minkowski space is
assigned the energy E = -1/4G, while the upper bound on the energy is set to
zero. Any variational principle with a boundary term built only from the
extrinsic and intrinsic curvatures of the boundary is shown to lead to the same
result. Interestingly, our result is not the flat-space limit of the
corresponding energy -1/8G of 2+1 anti-de Sitter space.
