Within the same month while I was cleaning my chain (before a long +50 mi beach ride and after) I got my right index finger caught in the chainring and barely nipped it. Nasty little cut. And the other nasty little bite on the tip of my left thumb. No stitches but there was an okay-amount of blood.
Ugh so dumb! I'm never ever going to clean my chain while its on my bike! Nowadays I just take the chain off and let it sit in degreaser overnight.