In a medium saucepan over medium heat combine the heavy cream and milk. Bring the mixture to a simmer stirring occasionally.
In a small bowl, whisk together the sugar and egg yolks. Set aside.
Remove the milk and heavy cream mixture from the heat. Pour in about 1 cup of the hot liquid to the egg and sugar mixture. Whisk together quickly. When combined well, pour the egg mixture back into the saucepan with the hot milk and cream. Stir to combine. Cook, stirring constantly over medium to low heat until the mixture is thick enough to coat the back of a wooden spoon. Transfer to a large bowl, add the vanilla and stir in. Cover with plastic wrap, pressing the plastic wrap directly on the custard mixture. Chill completely.
Follow the directions on your ice cream machine. Add the chocolate chips at the last few minutes while the ice cream churns in the machine. Pour into a freezer safe plastic container and allow to set for 2-3 hours.