  Manifestation of chiral excitons on surfaces of topological insulator thin
film with magnetically induced energy gap in the surface spectrum in
magnetooptical Kerr and Faraday effects is analyzes. Excitonic contribution to
a surface optical conductivity tensor is calculated. Chiral excitons contrary
to conventional ones resonantly contribute to Hall conductivity due to lack of
the symmetry between the states with opposite angular momentum. They can lead
to considerable enhancement of Faraday angle and ellipticity of transmitted
electromagnetic wave. Chiral excitons cause decrease of Kerr angle and
prominent signatures in ellipticity of reflected electromagnetic wave.
Conditions for experimental observation of described effects are discussed.
