  We develop a non-perturbative method to calculate the density of states (DOS)
of the fluctuating gap model describing the low-energy physics of electrons on
a disordered Peierls chain. For real order parameter field we calculate the DOS
at the Fermi energy exactly as a functional of the disorder for a chain of
finite length L. Averaging rho (0) with respect to a Gaussian probability
distribution of the Peierls order parameter, we show that in the thermodynamic
limit the average DOS at the Fermi energy diverges for any finite value of the
correlation length above the Peierls transition. Pseudogap behavior emerges
only if the Peierls order parameter is finite and sufficiently large.
