In some unusual cases, you may not control Perplexing Chimera when its triggered ability resolves (perhaps because the triggered ability triggered again and resolved while the original ability was on the stack). In these cases, you can exchange control of Perplexing Chimera and the spell that causes the ability to trigger, even if you control neither of them. If you do, you’ll be able to change targets of the spell, not the spell’s new controller.