I can’t recall ever seeing a Burger Chef restaurant back then. My family moved around the country several times over the years in the 70’s.
It’s possible they were operating in regions where there wasn’t a Burger King, and hence could offer the same Coca Cola movie tie-in promotions.
When I lived in New Jersey back in the late 70’s there were no Kentucky Fried Chicken locations to be found. But there was a burger chain called Gino’s that offered KFC food in addition to their own menu. That massively confused me as a kid. 😉
https://en.wikipedia.org/wiki/Gino’s_Hamburgers
JEDIT:I swear I saw the posters at BK too. I never got one for some reason. One wall in my room was already covered in SW posters and newspaper clippings. Still have all my glasses though. 😃