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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 ona disordered Peierls chain. For real order parameter field we calculate the DOSat the Fermi energy exactly as a functional of the disorder for a chain offinite length L. Averaging rho (0) with respect to a Gaussian probabilitydistribution of the Peierls order parameter, we show that in the thermodynamiclimit the average DOS at the Fermi energy diverges for any finite value of thecorrelation length above the Peierls transition. Pseudogap behavior emergesonly if the Peierls order parameter is finite and sufficiently large.Comment: 4 pages, 2 figures; one more reference added; final version to appear  in Phys. Rev. Lett. (Feb. 1999

Singularities and Pseudogaps in the Density of States of Peierls Chains