In early D&D, both chainmail and plate armor were considered metal armor, and to slow the wearer to 60' per turn. Chainmail cost 40gp, and plate armor 60gp. Their encumbrance was 400 or 500 coins apiece. Other than these very minor differences, chainmail granted a base AC of 5, and plate armor 3. All classes that allow wearing chainmail, also allow wearing plate armor.
I'm referring to Moldvay and Mentzer here, feel free to adjust my wording accordingly.
When would you ever want to wear chainmail instead of plate armor?