A purple material chest is an item in Evony TKR (The King's Return). It can be found after killing certain monsters or bosses, with some of them listed below.
The description of Purple Material Chest in Evony TKR says:
Open to receive a random lv4 Equipment material.
Purple Material Chest is known to drop from a number of bosses or monsters upon killing, including Senior Bayar Knight and Junior Knight Bayard.
Note: This list may be incomplete.