Mechanical flexibility in single crystals of covalently bound materials is a fascinating and poorly understood phenomenon. We present here the first example of a plastically flexible one‐dimensional (1D) coordination polymer. The compound [Zn(μ‐Cl)2(3,5‐dichloropyridine)2]n is flexible over two crystallographic faces. Remarkably, the single crystal remains intact when bent to 180°. A combination of microscopy, diffraction, and spectroscopic studies have been used to probe the structural response of the crystal lattice to mechanical bending. Deformation of the covalent polymer chains does not appear to be responsible for the observed macroscopic bending. Instead, our results suggest that mechanical bending occurs by displacement of the coordination polymer chains. Based on experimental and theoretical evidence, we propose a new model for mechanical flexibility in 1D coordination polymers. Moreover, our calculations propose a cause of the different mechanical properties of this compound and a structurally similar elastic material.