From Answers From a Bicycle Mechanic

This appeared in the comments section:
Doyle is of course being fatuous. However his exposition raises a certain etymological quandary. How does one express the possessive form in this case? The proper spelling of the chain is Popeyes Chicken (as noted once in a Times article the founder lamented that he was too poor to afford an apostrophe).

Therefore one can only conclude that the possessive form in this case would be best expressed as “Popeyes Chicken’s gravy.”
— Baron Vanderbilt Steiner Houndstooth II