Human teeth, that is, not the teeth on the ring or cog. Tim Kelton of Wichita Falls, Texas, was commuting on his singlespeed bicycle when his chain snapped and sent him over the bars. See the gruesome aftermath here. "However expensive that derailleur and a few gears would have been, " Kelton writes, "this is more."
The only time I've snapped a chain is with a dérailleur-equipped bike. It beat my rear dérailleur into little bits before spooling around the rear cog and locking up my rear wheel in heavy traffic, but I managed to stay upright and avoided injury to my teeth or the rest of my face.
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Ouch. The only time I broke a chain was on a track bike at the velodrome down near Ft. Lauderdale. I was out of the saddle doing a sprint coming down off the bank when all of a sudden there was no more resistance on the pedal. My balance was totally thrown off by the quick acceleration of the foot through the rest of the pedal stroke and I when straight down. The concrete surface was just smooth enough for me to slide on my butt for about 20 feet. The spandex in my shorts melted (I could see the singed edges around the big hole) and I got a huge case of road rash conveniently right on the part of the cheek that makes contact with whatever you're trying to sit on. Kept all of my teeth, though. This post was like driving past a car accident on the highway, I couldn't help but look at the photos... Thanks for sharing.