  With the example of Proxima Centauri we discuss the feasibility of detecting
terrestrial planets (1 to a few M_Earth) using the high precision radial
velocity (RV) technique. If a very high RV precision for M stars is achieved
even planets with these extremely low masses become detectable. For Proxima Cen
(M5V), one of the prime targets of our M-stars planet search program using the
UVES spectrograph & iodine cell at the ESO VLT UT2, we obtain a long term RV
precision of 2.5 m/s. Based on numerical simulations we determine that this
level of precision would have already allowed us to detect planets with m sin i
= 4 to 6 M_Earth inside the habitable zone of Proxima Cen.
