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High spin states of odd A 81Br were populated using the 82Se(4He, p4n) reaction with the beam energy of 65 and 68 MeV. A pair of nearly degenerate negative parity bands were observed in this nuclues, as well as a negative parity dipole band. Based on the experimental characters of these bands, they were respectively interpreted as a pair of chiral doublet bands based on the π(fp, g9/2g9/2) configuration and a stapler band. The interpretation was supported by the multiparticle rotor model and the self-consistent tilted axis cranking covariant density functional theory calculations. The present work suggests a new chiral configuration in the nuclear system, and provides the evidence for the coexistence of chiral doublet bands and stapler band in 81Br.