  We present the first determination of the proper motion of the neutron star
low mass X-ray binary {Cen X-4} measured from relative astrometry of the
secondary star using optical images at different epochs. We determine the
Galactic space velocity components of the system and find them to be
significantly different from the mean values that characterize the kinematics
of stars belonging to the halo, and the thin and the thick disc of the Galaxy.
The high metallicity of the secondary star of the system rules out a halo
origin and indicates that the system probably originated in the Galactic disc.
A statistical analysis of the galactocentric motion revealed that this binary
moves in a highly eccentric ($e\simeq 0.85\pm0.1$) orbit with an inclination of
$\simeq 110^\circ$ to the Galactic plane. The large Galactic space velocity
components strongly support that a high natal kick as a result of a supernova
explosion could have propelled the system into such an orbit from a birth place
in the Galactic disc. The high Li abundance in the secondary, comparable to
that of stars in star forming regions and young stellar clusters like the
Pleiades, may suggest a relatively recent formation of the system. Following
the orbit backwards in time, we found that the system could have been in the
inner regions of the Galactic disc $\sim$100--200 Myr ago. The neutron star
might have formed at that moment. However, we cannot rule out the possibility
that the system formed at a much earlier time if a Li production mechanism
exists in this LMXB.
