  High-velocity halo stars provide important information about the properties
of the extreme Galactic halo. The study of unbound and bound Population II
stars permits us to better estimate the mass of the halo.} {We carried out a
detailed spectroscopic and kinematic study and have significantly refined the
distance and the evolutionary state of the star. Its atmospheric parameters,
chemical abundances and kinematical properties were determined using
high-resolution optical spectroscopy and employing the
local-thermodynamic-equilibrium model atmospheres of Kurucz and the spectral
analysis code {\sc moog}. We found that CD-62$\degr$1346 is a metal-poor
([Fe/H]=$-$1.7) evolved giant star with $T_{\rm eff}=5300$ K and $\log g=1.7$.
The star exhibits high carbon and s-element abundances typical of CH stars. It
is also a lead star. Our kinematic analysis of its 3D space motions shows that
this star has a highly eccentric ($e=0.91$) retrograde orbit with an
apogalactic distance of $\sim 100$ kpc, exceeding by a factor of three the
distance to the Magellanic Clouds. The star travels with very high velocity
relative to the Galactocentric reference frame ($V_{\rm GRF}=570$
km\,s$^{-1}$). CD-62$\degr$1346 is an evolved giant star and not a subgiant
star, as was considered earlier. Whether it is bound or unbound to the Galaxy
depends on the assumed mass and on the adopted Galactic potential. We also show
that the star HD 5223 is another example of a high-velocity CH star that
exceeds the Galactic escape velocity. Possible origins of these two
high-velocity stars are briefly discussed. CD-62$\degr$1346 and HD 5223 are the
first red giant stars to join the restricted group of hypervelocity stars.
