I grew up in Southern Illinois and Burger Chef was a dozen miles away. That still made it the closest fast food chain around. It is also the first time I ever had fast food.
I looked up what happened to Burger Chef as they all disappeared about twenty years ago. We used to have a Sandee's burger chain in town, but Hardees bought them out in the mid 70's. Below is what I found on a web page devoted entirely to Burger Chef:
General Foods sold Burger Chef to Hardee's in 1982. It was at this time most Burger Chefs were converted to Hardee's outlets, many were closed or sold-especially those with a Hardee's location nearby. Less than 100 Burger Chef locations were left.
The last known Burger Chef was closed in 1996, located in Cookville, TN. There are restaurants operating today under the name Burger Chef, but have no connection with the original chain.