Place popcorn in a lightly greased large mixing bowl; set aside.
Combine sugar, molasses, butter, and vinegar in a small Dutch oven. Bring to a boil, stirring until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches hard ball stage (250°).
Remove from heat; stir in soda. Pour syrup over reserved popcorn; stir until all popcorn is coated. Cool slightly, and shape into 3-inch balls.