It isn't going to whip around - it is too far embedded into the tree on that one side. I'd cut the top of 1 link with bolt cutters or an angle grinder. That may (but probably not) weaken it enough that it pulls open if it is under excessive tension. When that doesn't loosen it enough, I'd probably go to another link and cut it at one end, then the other end of the same link.
Be careful to to pull off bark all the way to the inner bark (cambium) when removing the chain. If you are going to cause more damage to a small portion of the tree, It is best to let the tree "swallow" the chain for a few inches rather than damage the tree more. But it looks like that will probably come off it you are gentle with it.