  We explore the phase diagram of strongly interacting matter with massless u
and d quarks as a function of the strange quark mass m_s and the chemical
potential mu for baryon number. Neglecting electromagnetism, we describe the
different baryonic and quark matter phases at zero temperature. For quark
matter, we support our model-independent arguments with a quantitative analysis
of a model which uses a four-fermion interaction abstracted from single-gluon
exchange. For any finite m_s, at sufficiently large mu we find quark matter in
a color-flavor locked state which leaves a global vector-like SU(2)_{color+L+R}
symmetry unbroken. As a consequence, chiral symmetry is always broken in
sufficiently dense quark matter. As the density is reduced, for sufficiently
large m_s we observe a first order transition from the color-flavor locked
phase to a color superconducting phase analogous to that in two flavor QCD. At
this unlocking transition chiral symmetry is restored. For realistic values of
m_s our analysis indicates that chiral symmetry breaking may be present for all
densities down to those characteristic of baryonic matter. This supports the
idea that quark matter and baryonic matter may be continuously connected in
nature. We map the gaps at the quark Fermi surfaces in the high density
color-flavor locked phase onto gaps at the baryon Fermi surfaces at low
densities.
