Heat oven to 400°F. Bake pie crust as directed on package for one-crust baked pie shell. Cool completely.
Meanwhile, in 2-quart saucepan, cook milk and pudding mix over medium heat 5 to 8 minutes or until mixture comes to a full boil, stirring constantly. Remove from heat. Add chocolate chips; stir until melted and smooth. Pour into medium bowl; cover surface of pudding with plastic wrap. Refrigerate about 1 1/2 hours or until cold.
Spoon and spread evenly in cooled crust. Refrigerate at least 4 hours until set. Top each serving with whipped topping; garnish with chocolate curls. Cover and refrigerate any remaining pie.