Treasure Chests can be found all over the world. They contain various provisions, treats, weapons and armor, or numerous amount guilders that are helpful to Oliver and his team throughout his journey.
The Telling Stone is invaluable in the task of tracking down stray chests.
Red Chests are standard treasure chests. While there are hidden red chests in the overworld (discovered easily using Kublai's Seek Fortune spell), you find a few in the dungeons you roam.
Red chests may be opened by Oliver at any time, but the items within are generally of low-level quality.
Blue Chests are magically locked treasure chests that Oliver can open using the Spring Lock spell.
Blue chests are found in dungeons and other interior areas (like towns, caves, etc.). Horace's Chart Chests spell (complete Horace's Riddles to earn it in Hamelin) will let you find all manner of chests in interior areas.
Green Chests are magically locked treasure chests that Swaine can open using his lockgun. To do that, you need to locate a spot where Swaine can fire the weapon while facing the front of the green chest. That clue should help you narrow down the spots you need to search for a good shooting spot.
Green chests are found in dungeons and other interior areas (like towns, caves, etc.). Horace's Chart Chests spell will let you find all manner of chests in interior areas.
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 will let you find all of them with ease and patience.