We report on the progress of a program to search for extra-solar planets using high precision radial velocity (RV) measurements taken at the European Southern Observatory. Instrumental errors in the radial velocity measure are minimized by placing a temperature stabilized molecular iodine absorption cell in front of the entrance slit to the spectrograph. This imposes an iodine absorption spectrum on top of the stellar spectrum. All stellar radial velocity shifts are measured with respect to the iodine absorption spectrum. The current program consists of a sample of 26 F, G, and K dwarfs and 1 dMe star. Radial velocity measurements taken since November 1992 indicate that a typical longterm radial velocity precision for this program is about 18 m s-1. One of our program stars, &tgr; Cet, shows constant radial velocity variability with a scatter of 6 m s-1. Representative radial velocity measurements are given for three stars showing no significant radial velocity variations, three stars showing variations indicative of low mass companions, and for the triple system α Cen. The radial velocity measurements of α Cen A and B are consistent with the astrometric orbital solution, although the data points have a slightly steeper slope than the calculated orbit. Continued radial velocity monitoring of this star should eventually result in a better orbital solution. ¿ American Geophysical Union 1996