Three ΔI=1 bands with the πg_{9/2}⊗νg_{9/2} configuration have been identified in _{35}^{74}Br_{39}. Angular distribution, linear polarization, and lifetime measurements were performed to determine the multipolarity, type, mixing ratio, and absolute transition probability of the transitions. By comparing these experimental observations with the corresponding fingerprints and the quantum particle rotor model calculations, the second and third lowest bands are, respectively, suggested as the chiral partner and one-phonon wobbling excitation built on the yrast band. The evidence indicates the first chiral wobbler in nuclei.