A Composite Chiral Pair of Rotational Bands in the Odd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>Nucleus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>135</mml:mn></mml:mmultiscripts></mml:math>

High-spin states in 135Nd were populated with the 110Pd(30Si,5n)135Nd reaction at a 30Si bombarding energy of 133 MeV. Two DeltaI=1 bands with close excitation energies and the same parity were observed. These bands are directly linked by DeltaI=1 and DeltaI=2 transitions. The chiral nature of these two bands is confirmed by comparison with three-dimensional tilted axis cranking calculations. This is the first observation of a three-quasiparticle chiral structure and establishes the primarily geometric nature of this phenomenon.