A deployable robotic arm can be a useful tool for mobile systems to widen accessible areas without removing mobility. For practical use, the deployable robotic arm needs to satisfy two requirements: a high extension–compression ratio and robust structural stiffness against the environment. To this end, this paper suggests, for the first time, an origami-inspired zipper chain to achieve a highly compact, one-degree-of-freedom zipper chain arm. The key component is the foldable chain, which innovatively increases the space-saving capability in the stowed state. The foldable chain is fully flattened in the stowed state, allowing for storage of many more chains in the same space. Moreover, a transmission system was designed to transform a 2D flat pattern into a 3D chain shape in order to control the length of the origami zipper. Additionally, an empirical parametric study was performed to choose design parameters to maximize the bending stiffness. For the feasibility test, a prototype was built and performance tests were executed in relation to extension length, speed, and structural robustness.