One new pair of positive-parity chiral doublet bands have been identified in the odd-A nucleus 135Nd which together with the previously reported negative-parity chiral doublet bands constitute a third case of multiple chiral doublet (MχD) bands in the A ≈ 130 mass region. The properties of the MχD bands are well reproduced by constrained covariant density functional theory and particle rotor model calculations. The newly observed MχD bands in 135Nd represents an important milestone in supporting the existence of MχD in nuclei.