  At a critical finite chemical potential and low temperature QCD undergoes the
chiral restoration phase transition. The folklore tradition is that
simultaneously hadrons are deconfined and there appears the quark matter. We
demonstrate that it is possible to have confined but chirally symmetric hadrons
at a finite chemical potential and hence beyond the chiral restoration point at
a finite chemical potential and low temperature there could exist a chirally
symmetric matter consisting of chirally symmetric but confined hadrons. If it
does happen in QCD, then the QCD phase diagram should be reconsidered with
obvious implications for heavy ion programs and astrophysics.
