  We show how to use dimensional regularization to determine, within the
Arnowitt-Deser-Misner canonical formalism, the reduced Hamiltonian describing
the dynamics of two gravitationally interacting point masses. Implementing, at
the third post-Newtonian (3PN) accuracy, our procedure we find that dimensional
continuation yields a finite, unambiguous (no pole part) 3PN Hamiltonian which
uniquely determines the heretofore ambiguous ``static'' parameter: namely,
$\omega_s=0$. Our work also provides a remarkable check of the perturbative
consistency (compatibility with gauge symmetry) of dimensional continuation
through a direct calculation of the ``kinetic'' parameter $\omega_k$, giving
the unique answer compatible with global Poincar\'e invariance
($\omega_k={41/24}$) by summing $\sim50$ different dimensionally continued
contributions.
