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Hidden chests appear throughout Skyrim, but are invisible, and usually can only be opened by exploiting bugs. One example is the invisible chest under the Skyforge. It can only be reached by leaping over the walls and falling "under" the floor. These chests contain leveled loot, such as soul gems, enchanted weapons and armor, and a good amount of gold.
These chests are actually shopkeeper chests. The one under the skyforge is Eorlund Gray-Mane's shop chest and there is another one by Iron-Breaker Mine that belongs to Ahkari of the Khajiit Caravan's. There is one also hidden outside Markath near the bridge.
I located a chest directly east of Fort Greymoor in a destroyed house. When looking towards Fort Greymoor in the house you can make out the top of the chest beneath the broken floor. No real notable loot, just some gold and gems.
In the Winterhold Inn there are 2 chests, directly under the floor while standing in front of the innkeeper there is one chest with mostly food-type of loot and a small amount of gold. Second, go to the closest room to him on the right side (facing him) under the bed in that room there is a chest with many Spell Tomes and a random assortment of full and empty Soul Gems, unknown how to obtain them from a non-PC standpoint, but there also is a staff of Arcane Authority located behind the counter with the book "Words of Clan Mother Ahnissi."