High-spin states in Cs124 were populated in the Ni64(Ni64,p3n) reaction and the Gammasphere detector array was used to measure γ-ray coincidences. Both positive- and negative-parity bands, including bands with chiral configurations, have been extended to higher spin, where a shape change has been observed. The configurations of the bands before and after the alignment are discussed within the framework of the cranked Nilsson-Strutinsky model. The calculations suggest that the nucleus undergoes a shape transition from triaxial to prolate around spin I≃22 of the positive-parity states. The alignment gain of 8â.,, observed in the positive-parity bands, is due to partial alignment of several valence nucleons. This indicates the absence of band crossing due to paired nucleons in the bands.