  We formulate and analyze the Hamiltonian dynamics of a pair of massive
spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the
system to a conical infinity, isometric to the infinity generated by a single
massive but possibly spinning particle. The reduced phase space \Gamma_{red}
has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the
phase space of a Newtonian two-body system in the centre-of-mass frame, and we
find on \Gamma_{red} a canonical chart that makes this analogue explicit and
reduces to the Newtonian chart in the appropriate limit. Prospects for
quantization are commented on.
