In a saucepan blend together the sugar, cornstarch, and salt; add the cream, milk, and chocolate chips. Beat the egg and set aside for later.
Cook over medium heat until it starts to get thick and bubbly. Continue to cook another 2 minutes.
Remove the pudding off of the heat. Stir in a few spoons of the pudding mixture into the egg, one spoon at a time. Add the egg mixture to the pudding.
Return the pudding to the heat and continue to cook an additional 2 minutes. Remove from the heat and stir in the butter until melted. Add the vanilla and mix in well.
Spoon the pudding into dishes. Serve warm or chill before serving. Store in the refrigerator, cover with plastic wrap. The plastic wrap does not need to be touching the pudding.