Singlespeed bike for sprint tri?

I've got a fixie and at some point will ride it in a triathlon. You wouldn't really have any additional disadvantage over a geared bike that you don't already have (you'll spin it out going down hills and have to grind going up). But...you'll be the coolest kid at the race.

People over on ST talk occasionally about riding a fixed gear bike at an IM race...

USAT rules (plus safety & common sense) require a working brake on each wheel, otherwise don't see why not.

Thanks for the feedback. Once I pick out a race, I'll try to get an idea of how hilly the course will be and go from there.

I recently outfitted the bike in question with a set of aerobars and rode it yesterday for the first time since. I got pretty confident with them until about mile 16. I was confronted with a short (but steep) hill and boldly decided to try getting out of the saddle while holding the bar extensions. Mistake. Decelerated rapidly, lost control, and ate it (at about 5 mph, fortunately). 

 Long story short- I'm thinking gears may be the way to go, at least for my first time out.

Yeah, I guess hindsight is always 20/20, right? Lesson learned. Getting used to riding with aerobars is important, but not at the expense of the skin on your legs.

 The bike is a SS, by the way, not a fixie. Built up from an old steel Peugeot frame (ironically, a Peugeot "Triathlon". Solid, not too heavy, and fits like a glove.