Yes, but not during rush hour on CTA trains. The blackout hours are, IIRC, 7-9am and 4-6pm. You can always take your bike on the busses (on the front racks, not inside the bus) and on Metra trains.

The 606 and the Lakefront Trail are both fun, and there are lots of protected bike lanes inside the city.

Try to catch a bike bus or Critical Mass while you're here, or any of the group rides, really.

The others said everything I would have. Ill add the bike lane on dearborn is a lot of fun for riding through downtown.

Be sure to checkout !chibike@midwest.social I have a decent list of resources in the side bar, including the offical bike maps and the popular Mellow Streets Map.

Happy riding!