  We discuss in this note simultaneous existence of chiral symmetry breaking
and color superconductivity at finite temperature and density in a
Nambu-Jona-Lasinio type model. The methodology involves an explicit
construction of a variational ground state and minimisation of the
thermodynamic potential. There exists solutions to the gap equations at finite
densities with both quark antiquark as well as diquark condensates for the
"ground" state. However, such a phase is thermodynamically unstable with the
pressure being negative in this region. We also compute the equation of state,
and obtain the structure of the phase diagram in the model.
