Due to Shedd's popularity, you'll want to book your tickets at least a week in advance to increase the odds of getting tickets (and ideally early tickets: 9 and 10am are much better entrance times for a few of the exhibits) on the day of your choice.
Shedd will still get packed during the busiest days, but introducing timed tickets seems to have reduced the biggest crowds by spreading people out during the day. Mid-to-late afternoon tends to be much more sparse than earlier in the day. On heavy crowd days, I recommend getting to lunch by 11:30 at the latest, and I often try to get to the cafe by 11:00 to help ensure a wait is not too long, plus that tables are available..
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