Defensive garments composed of interlinking rings should correctly be referred to as "mail" or "mail armor". The common term “chain mail” is in fact a modern pleonasm (a lingual mistake meaning “the use of more words than are necessary to express an idea”: in this instance, both “chain” and “mail” refer to an object made of interlinking rings). In short, the term “chain mail” is saying the same thing twice.
Dirk H. Breiding
Department of Arms and Armor, The Metropolitan Museum of Art