Two-dimensional (2D) magnets show promising applications in spintronic devices and appeal increasing attention. CrI2, a counterpart of CrI3, is a magnetic van der Waals crystal. However, the structure of CrI2 at the monolayer limit is not well studied. Here, based on the density functional theory, we revealed the relationship between different phases of CrI2 monolayer and proposed a novel and stable chain structure. The one-dimensional (1D) CrI2 chain is a ferromagnetic semiconductor with robust electronic properties against twisting and tensile strain. Interestingly, the CrI2 chain exhibits superelasticity with a failure strain as large as 39%. In addition, both the magnetic moments on Cr atoms and the exchange energy increase with an increase in the tensile strain. Our results push magnetic ordering from 2D to 1D, which shows possible application prospects in magnetoelectric and spintronic devices.