The isoreticular analogue of the metal–organic framework UiO‐66(Zr), synthesized with the flexible trans‐1,4‐cyclohexanedicarboxylic acid as linker, shows a peculiar breathing behavior by reversibly losing long‐range crystalline order upon evacuation. The underlying flexibility is attributed to a concerted conformational contraction of up to two thirds of the linkers, which breaks the local lattice symmetry. X‐ray scattering data are described well by a nanodomain model in which differently oriented tetragonal‐type distortions propagate over about 7–10 unit cells.