A new form of matter - the nuclear condensate - may exist at
densities present in white dwarfs and in inertial confinement
experiments. This state has a number of unusual properties:
superconductivity by ions (not electrons), enhanced specific
heats and neutrino luminosities and unusual topological solitons.
On the theoretical side, it demonstrates a combination of the
Goldstone theorem and the Higgs phenomenon. We discuss some of
the properties of the nuclear condensate and the features that
make this strongly coupled system amenable to an analytical
approach.