  Proxima and Alpha Centauri AB have almost identical distances and proper
motions with respect to the Sun. Although the probability of such similar
parameters is in principle very low, the question as to whether they actually
form a single gravitationally bound triple system has been open since the
discovery of Proxima one century ago. Owing to HARPS high precision absolute
radial velocity measurements and the recent revision of the parameters of the
Alpha Cen pair, we show that Proxima and Alpha Cen are gravitationally bound
with a high degree of confidence. The orbital period of Proxima is
approximately 550 000 years. With an excentricity of 0.50 (+0.08 -0.09),
Proxima comes within 4.3 (+1.1 -0.9) kau of Alpha Cen at periastron. Its
orbital phase is currently close to apastron (13.0 +0.3 -0.1 kau). This orbital
motion may have influenced the formation or evolution of the recently
discovered planet orbiting Proxima as well as circumbinary planet formation
around Alpha Cen.
