Starting January 1, 2012, cyclists in Illinois will legally be allowed to proceed through a stop light if they have waited for a "reasonable time" and the light fails to change. This law does not make stop lights into stop signs for bicyclists, and it doesn't even affect cyclists in Chicago because the law excludes cities with more than two million people.
This law is designed to deal with stoplights that run on magnetic sensors designed to detect the presence of a car waiting at the light. Such traffic lights may stay red unless the sensors are triggered. As you might imagine, the sensors are designed to be triggered by automobiles, not bicycles. When a bicycle stops at an intersection controlled by a sensor the sensor may not be activated by the bicycle because the bicycle lacks enough mass to trigger the sensor. The light may never change becuase it isn't activated. The League of Illinois Bicyclists website gives some tips about how to trigger sensors if you are stuck at one of these intersections.
To be clear, you can't just stop at a stop light and then blow through the light. You have to wait a "reasonable time." While the act does not specify what a reasonable time is, the language and legislative history make it clear that this law is designed to deal with situations in which the light is malfunctioning or not detecting the bicycle.
See LIB's comments and suggestions on how to trigger signals here.
See the legislative history and language of the statute here.