  The possibility for existence of cold, dense chirally symmetric matter with
confinement is reviewed. The answer to this question crucially depends on the
mechanism of mass generation in QCD and interconnection of confinement and
chiral symmetry breaking. This question can be clarified from spectroscopy of
hadrons and their axial properties. Almost systematical parity doubling of
highly excited hadrons suggests that their mass is not related to chiral
symmetry breaking in the vacuum and is approximately chirally symmetric. Then
there is a possibility for existence of confining but chirally symmetric
matter. We clarify a possible mechanism underlying such a phase at low
temperatures and large density. Namely, at large density the Pauli blocking
prevents the gap equation to generate a solution with broken chiral symmetry.
However, the chirally symmetric part of the quark Green function as well as all
color non-singlet quantities are still infrared divergent, meaning that the
system is with confinement. A possible phase transition to such a matter is
most probably of the first order. This is because there are no chiral partners
to the lowest lying hadrons.
