Preheat oven to 350 F. Place popped popcorn in large bowl. Arrange graham cracker squares in bottom of 13 x 9-inch baking pan; trim slightly if necessary to fit pan. Sprinkle with 2 cups marshmallows and chocolate pieces. Put butter in 2-quart glass measuring cup. Microwave on HIGH until butter is melted, about 30 seconds. Stir in remaining 2 cups marshmallows until well coated. Microwave on HIGH until the marshmallows look puffy, about 1 minute; stir to melt completely. Pour marshmallow mixture over popcorn corn and mix well. Spread coated popcorn evenly over chocolate pieces in pan. Bake until marshmallows are puffy and appear to be melted, about 6 minutes in 250 F oven. Invert pan onto cutting board and cut into squares between graham crackers.