The jaywalking rules are less intimidating in Chicago than in some other places - for instance, in China, pedestrians aren't supposed to make eye contact with drivers (once eye contact is made, the driver figures the pedestrian will get out of the way) and in Egypt, pedestrians cut out into traffic, no matter how heavy, and miraculously arrive at the opposing sidewalk. Do not do this stateside.
The best location to jaywalk is at lights that normally have a pedestrian crossing because the light could change, validating your choice. Also, drivers will be more observant of what's going on at the intersection, and all lines of sight will be clear - drivers and bikers will see you, and just as importantly, you will see anything coming at you.
Yes - that's right. Bikes! A pedestrian's danger comes from both four and two-wheeled vehicles. Bicycle riders are faster than many people realize and getting hit by a bike is NOT something you want to encounter.
The other option for jaywalking is in the middle of the street. This can be annoying for drivers, because at the corner there is probably a stop sign - why not cross there? Be extra careful if there are cars parked on the street. They make both oncoming traffic and you less visible.
No matter where you choose to live life on the wild side, you should make sure there's no oncoming traffic and commit. If a vehicle suddenly appears out of nowhere, or if you gauged its speed wrong, don't play frogger. Acknowledge the driver with a smile and a wave, and keep going