Do they have valet parking

Yes. From website: Take advantage of valet parking during your hotel stay or visit to downtown Chicago. Overnight parking includes in-and-out privileges for your convenience. Please note: The parking garage has a maximum height clearance of 6’ 5”. For hotel guests: 0–1 hour $26 1–2 hours $28 2–6 hours $35 6–24 hours $72 For guests of NoMI: 0–4 hours $21 For guests of special events: $27

Its very likely that the hotel does.