Place popcorn in a large bowl or roasting pan. Lightly grease a large baking sheet. Set aside.

Combine the butter, corn syrup and white chocolate chips in a large saucepan over medium heat. Bring to a boil, stirring constantly. Add the marshmallows and continue stirring until everything is melted and smooth.

Pour the white chocolate/marshmallow mixture over the popcorn and stir until evenly coated. Let stand 1-2 minutes, until coating is slightly cooled but still soft (you should still be able to stir it). Gently fold in the chocolate pieces.

Spread popcorn onto the prepared baking sheet and cool until set. The popcorn should be chewy and soft when set, but not sticky.