We formulate and analyse 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 _red has dimension four and topology ³ × S ¹ . _red is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on _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.