We report on the crystal structure of the quantum magnet ͑CuCl͒LaNb 2 O 7 that was controversially described with respect to its structural organization and magnetic behavior. Using high-resolution synchrotron powder x-ray diffraction, electron diffraction, transmission electron microscopy, and band-structure calculations, we solve the room-temperature structure of this compound ͓␣-͑CuCl͒LaNb 2 O 7 ͔ and find two high-temperature polymorphs. The ␥-͑CuCl͒LaNb 2 O 7 phase, stable above 640 K, is tetragonal with a sub = 3.889 Å, c sub = 11.738 Å, and the space group P4 / mmm. In the ␥-͑CuCl͒LaNb 2 O 7 structure, the Cu and Cl atoms are randomly displaced from the special positions along the ͕100͖ directions. The  phase ͑a sub ϫ 2a sub ϫ c sub , space group Pbmm͒ and the ␣ phase ͑2a sub ϫ 2a sub ϫ c sub , space group Pbam͒ are stable between 640 K and 500 K and below 500 K, respectively. The structural changes at 500 and 640 K are identified as order-disorder phase transitions. The displacement of the Cl atoms is frozen upon the ␥ →  transformation while a cooperative tilting of the NbO 6 octahedra in the ␣ phase further eliminates the disorder of the Cu atoms. The low-temperature ␣-͑CuCl͒LaNb 2 O 7 structure thus combines the two types of the atomic displacements that interfere due to the bonding between the Cu atoms and the apical oxygens of the NbO 6 octahedra. The precise structural information resolves the controversy between the previous computation-based models and provides the long-sought input for understanding ͑CuCl͒LaNb 2 O 7 and related compounds with unusual magnetic properties.