The Smart Chicago Collaborative put together a really good but incomplete list of civic technology groups and resources. Below are some of these resources. Please add anything that they missed!

Chicago Code for America Brigade

A "brigade" is a local chapter of Code for America, a national civic technology nonprofit based out of San Francisco. They run a weekly Open Government Hack Night.

Free Geek Chicago

This nonprofit provides electronics repair and recycling services, low-cost computers, free computer literacy training, and more. (See also: Free Geek Portland)

Open Gov Chicagoland

A government transparency and civic innovation group. 

Data Potluck

A data potluck! Come learn about what people are doing!

Connect Chicago

These folks work in the realm of digital divide--both access to hardware and access to computer literacy skills.

...there are way more resources here. Please add!