MICROWAVE chocolate and milk in large microwaveable bowl on HIGH 2 min.; stir until chocolate is completely melted. Cool 20 min. or to room temperature, stirring occasionally.
ADD sugar and vanilla to whipped topping; stir until well blended. Add half of the whipped topping mixture to chocolate mixture; stir gently until well blended. Add remaining whipped topping mixture; mix lightly. Spoon into crust.
REFRIGERATE 4 hours or until ready to serve. Store leftover pie in refrigerator.