I've only eaten at their Shake Shack in the the lower level of the hotel, but I saw their hotel restaurant is listed on Resy.
Not sure how many people hold the Amex Delta Platinum or Reserve but figured this may be useful for some.

https://resy.com/cities/chi/chicago-...-02-27&seats=2

On an unrelated note, Hyatt announced many hotels were changing award categories on March 26. I was praying that CAA would go from 5 to 4, as it once was. Alas, it wasn't meant to be.
I was also bummed that the Thompson Chicago is going from 4 to 5. If you've never stayed and are looking for a good place to burn a certificate, I highly recommend it.

https://world.hyatt.com/content/gp/e...t-updates.html