  We present the detailed properties of a self-consistent crystalline chiral
condensate in the massless chiral Gross-Neveu model. We show that a suitable
ansatz for the Gorkov resolvent reduces the functional gap equation, for the
inhomogeneous condensate, to a nonlinear Schr\"odinger equation, which is
exactly soluble. The general crystalline solution includes as special cases all
previously known real and complex condensate solutions to the gap equation.
Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with
this inhomogeneous chiral condensate, and the exact spectral properties are
derived. We find an all-orders expansion of the Ginzburg-Landau effective
Lagrangian and show how the gap equation is solved order-by-order.
