It alludes to the fact that Popeye's originated in New Orleans, the "Birth Place of Jazz" or so they say. And what's more symbolic of Jazz music than the Saxophone?
Personally, I like Popeyes, and waited to try it out until they finally built a restaurant on the "white" side of town so I'd be sure to have my car waiting there in it's parking spot when I got back.
It's ok as far as chicken goes, and better than Col. Sanders. If you have high cholesterol or triglycerides, stay away and eat a salad at home instead.
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