How do I untangle a roadbike chain while it's still on the bike?

Alright, I'll admit, I was a little drunk when I started this little DIY endeavor. That said, one of my links was stuck so I decided to soak the chain overnight in solvent so I could butter it up this morning to ride. Rather than hammering out a link and taking it off of the bike itself, I loosened the rear... show more Alright, I'll admit, I was a little drunk when I started this little DIY endeavor. That said, one of my links was stuck so I decided to soak the chain overnight in solvent so I could butter it up this morning to ride. Rather than hammering out a link and taking it off of the bike itself, I loosened the rear wheel out of the dropout and let the chain (and affected link) sit in the solvent. SOMEHOW it tangled itself overnight (seriously), and there are three "loops" in it. How can I untangle it without removing the chain? And no, I do not want to take it to a shop for this. Thanks in advance!
Update: Okay, edit. This is not my fixie, this is a 10 speed Bianchi Strada. That's why I didn't want to take it completely off. The chain itself is undamaged (unbent, the kink is now loosened). I, of course, looked up the nature of the solvent that I used, but you may be right, might be time for a new chain anyway.
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