  We use a variational procedure to study finite density QCD in an
approximation in which the interaction between quarks is modelled by that
induced by instantons. We find that uniform states with conventional chiral
symmetry breaking have negative pressure with respect to empty space at all but
the lowest densities, and are therefore unstable. This is a precisely defined
phenomenon which motivates the basic picture of hadrons assumed in the MIT bag
model, with nucleons as droplets of chiral symmetry restored phase. At all
densities high enough that the chirally symmetric phase fills space, we find
that color symmetry is broken by the formation of a <qq> condensate of quark
Cooper pairs. A plausible ordering scheme leads to a substantial gap in a
Lorentz scalar channel involving quarks of two colors, and a much smaller gap
in an axial vector channel involving quarks of the third color.
