Chicago has made a request for proposals from companies offering a bike sharing program. The city is considering a 500 bike program and a 1500 bike program, quite a bit smaller than the systems in Paris and Lyon.
Mayor Daley is excited, and that matters. You've probably heard about his bulldozing of their island airport overnight. He has a way to influence things. As the Tribune puts it:
Daley returned from a trip to England in the 1990s smitten by what he considered the beauty of the wrought iron fences of London, and the result is visible everywhere today: faux wrought iron fencing from one end of Chicago to the other.
On the controversy scale, bike sharing is probably closer to decorative fencing than bulldozing an airport, so this should be easy to make happen.
It's relatively easy to implement compared to other transportation systems, and the cost is low. The benefits have been discussed on this site many times, so I'll let a Chicagoan continue:
Some people ride their bikes to commuter rail stations near their homes, "but because Metra does not allow bikes on trains during rush hours, having these bikes available at the [downtown] Metra stations would be just fantastic," [Ed Barsoti of Illinois League of Bicyclists] said. "That would kind of complete the door-to-door trip."
For anyone new to this issue, I should point out that Toronto's Community Bicycle Network managed to implement a successful bike sharing program at a very low cost with no advertising. Toronto's government let it die.
In the meantime, a video about the success of the Lyon program, Vel'ov, has shown up on Youtube.