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Using the most recent kinematic and radial velocity data in the literature,we calculate the binding energy of Proxima Centauri relative to the center ofmass of the Alpha Centauri system. When we adopt the centroids of the observeddata, we find that the three stars constitute a bound system, albeit with asemi-major axis that is on order the same size as Alpha Centauri AB's Hillradius in the galactic potential. We carry out a Monte Carlo simulation underthe assumption that the errors in the observed quantities are uncorrelated. Inthis simulation, 44% of the trial systems are bound, and systems on the 1-3sigma tail of the radial velocity distribution can have Proxima currentlylocated near the apastron position of its orbit. Our analysis shows that afurther, very significant improvement in the characterization of the system canbe gained by obtaining a more accurate measurement of the radial velocity ofProxima Centauri.Comment: 10 pages total, 4 pages of text, 1 page of references, 3 figures, and  2 tables This article will be published in The Astronomical Journa

Are Proxima and α Centauri Gravitationally Bound?