This award availability gets you from Chicago O'Hare to London Heathrow in business class for 57,500 AAdvantage miles plus $738 in taxes and fees. The route typically prices out around 115,000 miles through American's program, so this represents a solid value for anyone with the miles to spare.
The catch: there's only one seat available at this price. That makes this a better fit for solo travelers or someone scouting ahead for a special trip. Families will need to keep searching for dates with more availability.
Keep in mind that the $738 in carrier-imposed surcharges and taxes is on the higher side, which is common for transatlantic flights arriving in the UK. Factor this into your overall cost calculation when deciding whether to book with miles or cash.
If you're flexible on dates, it's worth searching surrounding days to see if similar pricing opens up with more seats. Award availability to London tends to fluctuate, particularly as you get closer to peak summer travel.
How to book
Search and book directly through American Airlines: https://www.aa.com/booking/choose-flights/1