Here’s my guess. I did some Columbo-like research on the interwebs and discovered a defunct midwestern restaurant chain called ‘Chicken Unlimited’. Apparently it had a ton of locations back in the day.
TV Commercial:
https://youtu.be/4DxwvjP0_G4
Chicken Unlimited
with such a sexy/snappy name...I can't imagine why they are now defunct? Makes me think of the fictitious supermarket on Parks & Recreation, "Food & Stuff"