  We present differential radial velocity measurements of Proxima Centauri
collected over 4 years with the ESO CES with a mean precision of $54 ms^{-1}$.
We find no evidence of a periodic signal that could corroborate the existence
of a sub-stellar companion. We put upper limits (97% confidence) to the
companion mass ranging from 1.1 to 22 M_{Jup} at orbital periods of 0.75 to
3000 d, i.e. separations 0.008-2 AU from Prox Cen. Our mass limits concur with
limits found by precise astrometry (Benedict et al. 1998a and priv. comm.)
which strongly constrain the period range 50-600 d to 1.1-0.22 M_{Jup}.
Combining both results we exclude a brown dwarf or supermassive planet at
separations 0.008-0.69 AU from Prox Cen. We also find that, at the level of our
precision, the RV data are not affected by stellar activity.
