In a large saucepan, whisk together the sugar, cornstarch, cocoa powder, and salt until well combined. Whisk in the milk. Heat the mixture over medium-high heat, stirring constantly until it thickens and starts to bubble lightly, about 6 to 8 minutes. Remove from heat. Stir in the chocolate chips and vanilla extract.
Divide the pudding into six 4-ounce ramekins. Place a bit of plastic wrap or waxed paper ON the surface of the pudding to prevent a skin from developing. Refrigerate for several hours until cold. Serve with whipped cream if desired.
Promptly store leftovers in an airtight container in the refrigerator, for up to 3 days.Nutritional values are approximate and based on 1 serving.