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Purple Chests are magically locked treasure chests that Oliver can open using the Spring Lock spell, but only after you have access to the Miasma Marshes (rather late in the game).
Purple chests are found in dungeons but rarely in other interior areas (like towns, caves, etc.) although there are a few here and there with valuable items and equipment. Like all interior chests, Horace's Chart Chests spell (complete Horace's Riddles to earn it in Hamelin) will let you find all of them with ease and patience.
See Also
Ni no Kuni - TV Tropes