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

Resonant manifestations of chiral excitons in magnetooptical Faraday and Kerr effects in topological insulator film