I'm flying from LAX at 5am, and have a six hour layover in ORD (O'Hare, Chicago).
I am flying business to Heathrow on British Airways.
Where can I get a few hours of sleep?
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Hilton Chicago O'Hare offers day rooms:
Available for $79 on weekends and $99 on weekdays, the Day Room Package is available from 9:00 a.m. to 6:00 p.m
The hotel is connected directly to the terminal:
The award-winning Hilton Chicago O'Hare Airport is the only hotel situated on the airport's property. There is no need to take a cab or a shuttle bus since the hotel is connected to the airport terminals by underground pedways
Due to the insane, hypocritical prudishness of the USA, hourly rate hotels do not exist there because OMG someone might have sex out of wedlock and the wrath of God would smite everyone helping them.
That said, there are day rate hotels, for example at https://www.hotelsbyday.com . It says something about the situation that https://www.between9and5.com/ doesn't even list the Chicago O'Hare airport.