It would depend on the variety of chilis and the number I had to eat. If the challenge involved eating a few of the the chilis in your photograph, than yes I would take and win the bet and likely not feel uncomfortable. They look like Serranos (~15,000 Scoville Units) or Cayenne peppers (~40,000 Scoville Units), which very hot compared to other options. If the challenge involved eating a single Pequin (~75,000 Scoville Units) or Thai Pepper (~75,000 Scoville Units) I would do it and win, but wouldn't want to eat multiples. Hotter chilis or larger quantities just wouldn't be worth the $100 reward to me. A Naga Ghost pepper would probably send me running away screaming as I wouldn't dream of tackling a 1,000,000 Scoville Unit pepper for such a small prize. Those things are so powerful that India uses them in grenades to stop riots.

I love how really spicy food gives you a lift like a healthier version of caffeine. I grow and dry my own Pequin chilis at home to cook with. They are hot enough to leave blisters on your skin if get their juice on your bare skin for more than a few seconds.

I once entered my salsa in a competition and had one of the judges yell at me for bringing something so ridiculously hot. She gave me a 0 out of 10 vote because she was so mad. The funny thing was that I had deliberately made a milder version than usual in the hope of avoiding that reaction. I ended up winning 3rd prize in spite of it as the other judges really liked it.

When I bring the mild version of my infamous "Chili con Carnage" to a potluck, I put 72pt warning signs on all sides of the pot. Spicy food lovers rave about this dish, but invariably there is always one person who either doesn't know their limits or ignores the warning signs and ends up angry.

I keep these sauces on hand and cook with them often:
Mad Dog Inferno Hot Sauce (90,000 Scoville units of heat)
http://www.flickr.com/photos/j-p_engelund/2934104425/
It's great both as a condiment and as an ingredient. At first you taste a fantastic mildly spicy and smoky flavor, and then about 30 seconds after you swallow it you are hit by a blast of fire. People who use it as a condiment typically apply it by dipping a toothpick into the sauce and then rubbing the toothpick on their food.

Pure Cap (500,000 Scoville units of heat)
http://www.flickr.com/photos/davejenbarnes/26598765/
This stuff is only for mixing with other items. It's pure capsaicin suspended in oil and is applied using an eye dropper one drop at a time. If taken straight it would probably require medical attention, so if you buy it don't use it for jokes or accidentally get it on your skin.

To give you an idea of their heat, a Green Bell Pepper is rated at 0 Scoville units, a Jalapeno is at around 5,000 and a Habanero comes in at around 200,000 Scoville units.