I have come across multiple chests that will not let me open them. They have an eye in the middle which looks at me when I get close.
They look like this:
You must cast the Disillusionment charm so that you are invisible to the eyeball, letting you get close and open it. Note that you must cast this at a little bit of a distance (only a few metres) so it doesn't see you coming. You can then get close to the chest whilst invisible and open it.