Much like the hamburger, we may never know for sure who created America's first cheeseburger. Most credit Lionel Sternberger, who in the year 1924, at the tender age of 16, decided to slap a slice of American cheese (what else?) onto a cooking hamburger at his father's Pasadena, California sandwich shop, the Rite Spot. He liked it, and so did his dad, thus the cheeseburger was born. Or was it? See, they called it a "cheese hamburger," so that may disqualify them on a technicality.
The first sandwich to actually be called a "cheeseburger," was at a restaurant in Louisville, Kentucky called Kaelin's. Charles Kaelin claims to have invented the cheese-topped burger in 1934, because he wanted, according to local author Robin Garr, to "add a new tang to the hamburger." This is the earliest example of a menu claiming to be "the birthplace of the cheeseburger."
So, depending on how strong your feelings on semantics are, the cheeseburger was either invented in 1924, or in 1934. Why don't you have a cheeseburger, or cheese hamburger, and think it over.