  Using the most recent kinematic and radial velocity data in the literature,
we calculate the binding energy of Proxima Centauri relative to the center of
mass of the Alpha Centauri system. When we adopt the centroids of the observed
data, we find that the three stars constitute a bound system, albeit with a
semi-major axis that is on order the same size as Alpha Centauri AB's Hill
radius in the galactic potential. We carry out a Monte Carlo simulation under
the assumption that the errors in the observed quantities are uncorrelated. In
this simulation, 44% of the trial systems are bound, and systems on the 1-3
sigma tail of the radial velocity distribution can have Proxima currently
located near the apastron position of its orbit. Our analysis shows that a
further, very significant improvement in the characterization of the system can
be gained by obtaining a more accurate measurement of the radial velocity of
Proxima Centauri.
