By means of single-crystal neutron diffraction, an isostructural transition is observed at the N\'eel temperature of ${\text{CsCuCl}}_{3}$, a quasi-one-dimensional antiferromagnet with a helically modulated crystal structure that is built out of six ${\text{Cu}}^{2+}$ layers. Abrupt atomic displacements of about $0.01\text{ }\text{\AA{}}$ minimize the ferromagnetic interlayer superexchange interaction via the path Cu-Cl1-Cu that enters also the antiferromagnetic path Cu-Cl1-Cl2-Cu. The latter couples only one pair of ${\text{Cu}}^{2+}$ ions in each chlorine layer since all the other intralayer bonds either have much longer interatomic distances or include more than two intermediate Cl ions and, therefore, can be neglected. Thus, a spatial geometric frustration in this helically modulated stacked triangular lattice is provided by three Cu layers. Influences of the atomic displacements on the exchange energy, as well as the critical behavior of this spatially frustrated material, are discussed.