In a medium pot combine milk and vanilla pudding mix, place over medium heat whisking constantly. Bring to a boil while continuing to whisk the mixture.
In 3 medium bowls place white, dark and milk chocolate chips. Combine reserved chips together in a small bowl, mix and set aside.
Remove mixture from the heat and evenly divide the hot pudding over the 3 bowls. Wait 1 minute then whisk the mixture to incorporate and melt the chips into the pudding.
Set up 3 resealable bags into 3 large glasses so that it will be easy to pour the warm pudding into the bags. Pour the pudding into separate bags. Tie the bags closed with a twist tie. Place pudding into the refrigerator for 2 hours, or until pudding is chilled and set.
Cut off the corner of each bag. Pipe each of the pudding mixtures evenly into 6 champagne glasses starting with the dark chocolate, white chocolate and ending with milk chocolate.