Well, I only have one, maybe two 'private' chests that I know of, one was just to store essential supplies (food really) early on and doesn't need to be private anymore. I may have made that one not-private already, I don't remember.
The other one is a storage chest next to an abandoned mine entrance (which isn't the only entrance to the abandoned mine and the ravine system anymore anyways) which probably is private, but I can make that non-private. I just kind of forgot about it being a 'private' chest and just didn't want anybody to take the stuff out of there when I made it private.
Two chests near another abandoned mine entrance might be, but I don't think so.
Isn't there a command that lists how many registered chests you have?