  One new pair of positive-parity chiral doublet bands have been identified in
the odd-$A$ nucleus $^{135}$Nd which together with the previously reported
negative-parity chiral doublet bands constitute a third case of multiple chiral
doublet (M$\chi$D) bands in the $A\approx130$ mass region. The properties of
the M$\chi$D bands are well reproduced by constrained covariant density
functional theory and particle rotor model calculations. The newly observed
M$\chi$D bands in $^{135}$Nd represents an important milestone in supporting
the existence of M$\chi$D in nuclei.
