Chicago Mayor Rahm Emmanuel specified that the winning company would have to transport passengers and their luggage between the airport and downtown in 20 minutes or less.
Musk, the founder of Space X and Tesla Inc., has high credibility in the tech world for delivering on ideas that have stymied others.
Musk unveiled that undertaking last July, saying the Boring Company had received "verbal govt approval" to build a Hyperloop tube train system that would be capable of whisking passengers from NY to Washington in 29 minutes. Musk founded the company in the hope of alleviating city gridlock by building more tunnels, an endeavor that has set the company's engineers toward improving tunneling techniques. Better, but it still takes 40 minutes to make the trip.
The Boring Company has estimated the cost of the project to be $1bn, which would be entirely funded by it in exchange for all revenue from the system's transit fees, advertising, branding and in-vehicle sales.
The $250 million station beneath Block 37 was first envisioned as the hub of an express train system linking downtown to both O'Hare and Midway airports, but was abandoned in 2011 while only half-finished, after running well over budget.
A Boring Company spokesman said Thursday the company is "really excited" to work with the city.
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The Chicago and Los Angeles projects come as Musk wrestles with production problems for the rollout of the highly anticipated Tesla Model 3 sedan.
According to published reports, The Boring Co. has estimated the project would cost less than $1 billion.
The Chicago project generally would use already existing "electric skate" technology, though it would link them together in a form and length that is unique to this country.
"Mayor Emanuel is prioritizing the interests of billionaires and big corporations ahead of the very real and immediate needs of Chicago's taxpayers and neighborhoods", he said in a statement.
Musk's plan proposes a 16-passenger autonomous vehicle that can whip passengers at speeds up to 100 miles per hour through tunnels between the airport and downtown.
"We're taking a bet on a guy who doesn't like to fail - and his resources". The Boring Company released Wednesday renderings of what the underground system and rail cars would look like. The Loop's 18-mile route supposedly would cost passengers $20 to $25 per trip. The website says a skate could also hold "a single passenger vehicle".