Pop the popcorn according to package directions and set aside.
In a large saucepan, melt the butter over medium heat. Continue cooking until the butter begins to turn golden brown.
Add the marshmallows to the saucepan, stirring constantly until the marshmallows are fully melted and smooth.
Remove the saucepan from heat and stir in the vanilla extract.
Add the popped popcorn and Golden Grahams cereal to the marshmallow mixture. Fold gently until all the popcorn and cereal are evenly coated.
Allow the mixture to cool slightly until it is comfortable to handle. Lightly spray your hands with nonstick cooking spray.
Scoop about 1 cup of the popcorn mixture and shape it into a ball, pressing gently to hold its shape.
Sprinkle mini semisweet chocolate chips over the popcorn ball, pressing them in gently to adhere.
Place the finished popcorn balls on a sheet of waxed paper, parchment paper, or a silicone baking mat to cool and set.