High-spin states in 105 Rh were populated by the 96 Zr( 13 C, p3n) reaction at beam energies of 51 and 58 MeV, and studied using the EUROBALL IV γ-ray spectrometer and the DIAMANT charged particle array. A pair of nearly degenerate ΔI=1 three-quasiparticle bands with the same spins and parity have been observed. Comparison of the experimental results with tilted axis cranking calculations confirms the chiral character of the two bands, while arguments based on the excitation of particles within the πg9/2ν(h11/2)2 configuration of the yrast band and comparison with the previously observed γ band exclude the other possible interpretations. This is the first experimental evidence for three-quasiparticle chiral structure in the A ∼ 100 region, and the first simultaneous observation of a γ band and chiral partner bands in one nucleus.