Place both the chocolate and butter in a microwave-safe bowl. Heat at half power in 30 second increments until the chocolate and butter have melted. Stir until smooth and let it cool for 10 minutes.
Preheat oven to 350° F
Mix the sugar, egg and vanilla extract together in a bowl. Add the melted butter/chocolate mixture and stir. Add chocolate chips.
Divide the batter evenly between two 5 inch skillets. Place on a lined baking sheet to catch spills when baking.
Bake for 20 to 25 minutes or until a tooth pick placed in the center comes out with moist crumbs.
Serve warm with ice cream.