Bicycles are permitted on the 'L' (CTA trains) every weekday except from 7 am to 9 am and 4 pm to 6 pm (with certain exceptions where crowding is anticipated).
On Saturdays, Sundays and holidays (except when prohibited), bicycles are allowed on trains all day. If you board the train with your bicycle before the hours listed above and your trip extends into those hours, the CTA allows you to finish your trip.
Always be mindful of other passengers.
See also: Bike & Ride main page