Place the chocolate and butter in a microwave-safe bowl. Heat at half-power in 30-second increments until the butter is melted and the chocolate melts when stirred. Stir until smooth. Let cool for 10 minutes.
Preheat oven to 350°F (175°C).
Add the flour and salt to the chocolate mixture, and mix well.
In a separate bowl, combine the sugar, egg, and vanilla. Add to the chocolate mixture, stirring until combined. Stir in the chocolate chips.
Divide the batter evenly between two 5-inch skillets. Place on a lined baking sheet to catch any potential spills.
Bake 20 to 25 minutes, or until a pick inserted into the center comes out with moist crumbs. Do not over-bake.
Serve warm with ice cream or your choice of toppings.
Notes
If your skillets are well-seasoned, you shouldn't have to grease them. Otherwise, you may want to grease them lightly before adding the batter.