I thought at first that you were trying to reverse the chain, that is, make the inside, the outside. ( for wear purposes ) I see now that wasn't your original intent, but that is probably where you have ended up.

I think that when you try to untangle it, you are trying to untangle it the wrong way. You are trying to make the inside the outside. That is impossible without braking the chain. If you can't untangle it one way, try the other. Does this make sense? You can rotate something like a rope along its length when it is looped, but not a chain. Simplest answer is get a chain breaker and a master link.