Line a baking sheet with wax paper; set aside. Place the popcorn in a large bowl; set aside.
In a heavy medium pot, stir to combine the molasses, sugar, butter and vinegar. Bring to a boil over medium-high heat, then reduce to a simmer and cook until the mixture reaches 260 degrees F (hard ball stage) on a candy thermometer, 5 to 8 minutes. Let cool for about 5 minutes, then pour over the popcorn; fold and mix to coat using a rubber spatula. Let the popcorn cool slightly.
Coat your hands well with butter and form the popcorn mixture into 1/2-cup balls, squeezing to keep the popcorn together. Place on the prepared baking sheet and let sit until completely cooled and hardened, about 20 minutes.