The city of Chattanooga, Tennessee, is dangling wads of cash in front of nerdy innovators everywhere.

A mix of local and national investors have partnered to launch the Gig City Gig Tank and are offering $300,000 of cold, hard, start-up cash and prizes to be split among entrepreneurs and students with the best ideas for how to create the fastest internet in the world.

The catch: To claim the prize, you have to go to Chattanooga.

When we think of American tech innovation, places like the Silicon Valley and Seattle tend to come to mind more readily than Chattanooga. But maybe we should give Tennessee’s fourth largest city a bit more credit. Last year, the city-owned Electric Power Board (EPB) brought the country’s first gigabit-per-second fiber optic network to more than 150,000 households and businesses in a 600-square-mile radius.

Jack Studer of Lamp Post Group, a “venture incubator” backing the Gig Tank, told Wired.com that his parents, who live on a farm 35 miles outside of Chattanooga, have access to the network. If you’re suddenly feeling very envious of a couple of farmers in rural Tennessee, you should be — according to The New York Times, the gigabit network allows for connections 200 times faster than the average broadband speed in America.

But there are some major kinks to be ironed out. Chief among them is the price tag — GigaOm reported earlier this year that Chattanoogans pay more than $300 per month for gigabit service. Not so good compared to the $27 per month some South Koreans are paying for the same speed.

The idea of the Gig Tank isn’t to fix this problem, necessarily, but to give students and tech entrepreneurs a chance to use the network, which is not yet affordable or available on a wide scale, to design high-speed apps and businesses.

If you are one of the lucky few selected in what has been dubbed the Geek Hunt — a moniker chosen to evoke techiness and the Southern pastime of hunting, said Studer — the world is your oyster, and your oyster is a faster series of tubes than Sen. Ted Stevens could have ever imagined. The thousands of dollars of start-up cash should come in handy too, especially in a time when venture capital isn’t exactly growing on trees. The Gig Tank will give each of 10 entrepreneur teams $15,000 to work with, and at the end of the program the team with the best idea will take home $100,000. Ten to 15 students will compete for a $50,000 prize, but won’t receive any start-up cash on the front end.

And there’s still money in it for you even if you’re not the next Mark Zuckerberg or Jack Dorsey. In a promotional video calling for applicants, the Gig Tank hails geeks as the pioneers of the 21st century — successors to sea-faring explorers, westward-bound settlers, and astronauts. “But geeks are a furtive kind and can be difficult to track,” the video says, “so to find them, we need your help.”

The Gig Tank is asking people on Facebook or Twitter to tag friends who might be good candidates. A $1,000 finder’s fee will be awarded to anyone whose nominee applies and is chosen. Applicants can also nominate themselves.

When Wired.com asked about this approach, Studer explained that “if you can’t figure out how to tag yourself online, you’re not nearly geeky enough” for the Gig Tank.

It will be interesting to see the ideas that surface in Chattanooga during the program, which will run from May to August of 2012, but the most intriguing storyline is the gigabit plot.

Technically the gigabit-per-second technology can be used anywhere that has a comprehensive fiber optic network in place, but Americans are years, and perhaps decades, away from having it at their fingertips for an affordable price.

President Obama vowed to prioritize digital innovation in his State of the Union address earlier this year, and said “we will make it possible for business to deploy the next generation of high-speed wireless coverage to 98 percent of all Americans” in the next five years.

We’ll see — maybe Chattanooga is the unlikely first piece of the puzzle, but for now the U.S. is lagging behind countries like South Korea, whose average broadband speed is already 200 times faster than America’s. And by the end of 2012, South Korea plans to make a gigabit-per-second network accessible from every household in the country at a price that’s one-tenth of what Chattanoogans are currently paying.

So here’s a pat on the back, Chattanooga — nice work so far — but you and the rest of America have a steep hill to climb to get back to the top of the world of Internet innovation.

Image: The Gig Tank