Preheat oven to 170 C / Gas 3. Set six 175ml ramekins on a baking tray.
Pour cream, sugar and vanilla into a saucepan and place over medium heat. Stir to dissolve the sugar and heat until it begins to simmer, then remove from heat. Place egg yolks in a large bowl and slowly beat in the hot cream mixture, about 2 tablespoons at a time, until you have added approximately 250ml cream to the yolks. At this point, pour in the remaining cream and beat until smooth. Stir in the chocolate chips and set aside for 5 minutes.
Stir the mixture until the chocolate is smooth and evenly distributed. Pour into ramekins and bake in preheated oven until the centre is just set, 15 to 20 minutes. Remove from oven and allow to cool for 45 minutes, then place into the refrigerator and chill until cold, about 6 hours.
Place oven rack in highest position. Preheat grill.
Sprinkle the tops of each creme brulee with sugar until evenly coated, gently pour off excess sugar. Place ramekins onto a baking tray and place under the grill until the sugar bubbles and turns a light caramel brown. Serve immediately.