How does Chicago O'Hare's tower sequence aircraft at peak capacity?
Chicago runs simultaneous triple parallel approaches. And as soon as an aircraft clears the runway, another one is allowed to cross the threshold.

Chicago Tower actually does not do the bulk of the sequencing of aircraft. Chicago TRACON actually sequences the aircraft before they are handed to the Tower. Even before that, Chicago ARTCC begins to sequence inbound aircraft. Similarly, aircraft are handed to departure (TRACON) almost immediately after taking off. Departure procedures are optimized for safety and efficiency.

This figure breaks down runway usage percentage for arrivals and departures in April 2015 (7am - 10pm traffic)(source paper). It highlights the common westbound landing flow with triple parallel runways. You can also see two diverging runways used for the bulk of departures, with sporadic usage of others.



Note that this is all after an airport runway overhaul. Consider that 2014 saw almost a 10% decrease in operations from the year 2005. Having talked to controllers that have put in time at Chicago Tower, it is as crazy to handle as humanly possible.