Preheat oven to 325 degrees F.
Combine the cream, butter, and sugar in a medium saucepan, bring to a simmer over medium heat. Once the combination comes to a simmer, remove from the heat and add the chocolate chips. Cover the saucepan with a lid and allow the chocolate to melt. Once the chocolate has melted mix until smooth.
While the cream is coming to a simmer add the eggs to a large bowl. Beat until they thicken and turn light in color, about 2 to 3 minutes. Add the vanilla and salt and beat in.
Add a few tablespoons of the chocolate mixture to the eggs while mixing. You do not want to add too much so that you don't cook the eggs. When mixing the egg mixture gradually add the rest of the chocolate.
Spoon the pudding into six custard cups or ramekins evenly. Place the custard cups in a baking dish and fill the baking dish with water, so the water comes up halfway.
Place the baking dish in the preheated oven. Bake for 35 to 40 minutes or until the center is just about set.
Remove from oven and remove the pudding from the water, cool on a cooling rack. Cool until warm and ready to serve. If serving cold, cool completely and set in the refrigerator to chill for an hour or so.
Top with whipped cream if desired.