  We argue that in cold, dense quark matter, in the limit of a large number of
colors the ground state is unstable with respect to creation of a complicated
Quarkyonic Chiral Spiral (QCS) state, in which both chiral and translational
symmetries are spontaneously broken. The entire Fermi surface is covered with
patches of QCSs, whose number increases as the quark density does. The low
energy excitations are gapless, given by Wess-Zumino-Novikov-Witten model plus
transverse kinetic terms localized about different patches.
