We explain techniques for creating mathematical chain mail, by which we mean patterns made from identical linked ring shapes. Most chain mail currently in existence uses circular, or at least planar, rings which are linked in a variety of ways. By contrast, we show how a small nonplanar “wiggle” in the shapes permits a marvelous variety of woven patterns. We give formulas general enough to capture every possible periodic chain mail pattern, but admit that the issue of weaving and self-avoidance of the rings is a decidedly empirical one. We show photographs of 3D-printed chain mail as well as virtual images, created and rendered in Rhino using the Grasshopper plugin. We mention color symmetry in chain mail, as well as possibilities for covering surfaces in mail.