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William D. Cochran, Artie P. Hatzes (U. Texas), Martin K\"urster (ESO), Konrad Dennerl, Stephan D\"obereiner (MPI Garching)
We present the results of five years of precise radial-velocity monitoring of Proxima Centauri, from the European Southern Observatory. All of the data have been acquired using the ESO 1.4m Coudé Auxiliary Telescope and Coudé Echelle Spectrograph in La Silla. An I2 gas absorption cell is used as the velocity metric. This 11.05 magnitude M5V star is the faintest star on our ESO program list. Photon noise limits our velocity precision to about 65\,m\,s-1. Even at this level of precision, our data allow us to place significant limits on the presence of planetary-mass companions to our nearest stellar neighbor.