  We derive a new exact self-consistent crystalline condensate in the 1+1
dimensional chiral Gross-Neveu model. This also yields a new exact crystalline
solution for the one dimensional Bogoliubov-de Gennes equations and the
Eilenberger equation of semiclassical superconductivity. We show that the
functional gap equation can be reduced to a solvable nonlinear equation, and
discuss implications for the temperature-chemical potential phase diagram.
