  The problem of the Fermi--edge singularity in a one--dimensional
Tomonaga--Luttinger liquid is reconsidered. The backward scattering of the
conduction band electrons on the impurity--like hole in the valence band is
analyzed by mapping the problem onto a Coulomb gas theory. For the case when
the electron--electron interaction is repulsive the obtained exponent of the
one--dimensional Fermi--edge singularity appears to be different from the
exponent found in the previous studies. It is shown that the infrared physics
of the Fermi--edge singularity in the presence of backward scattering and
electron--electron repulsion resembles the physics of the Kondo problem.
