We had a Burger Chef in town. I went once with my mom, remember a small burger with too much mustard. The store went belly up soon afterwards.I am old enough (57) to remember when McDonald's had the red and white tiles and yellow arches, with the burger-headed guy on the sign like in the OP's pic. I was a little kid but can still recall it.
Someone mentioned the Red Barn.....I remember that too. How about Burger Chef, anyone recall that?
I vaguely recall the introduction of the Big Mac...I must have been 3 or 4 at the time, my dad came out to the car with it in the bag, we both took a bite, looked at each other, put it back in the bag drove the three miles down the road to Lobsterman and split a takeout container of shrimp.
"Don't tell your mother"