Heat oven to 450°F. Unroll pie crust into 9-inch pie plate, pressing against side and bottom of pie plate. Fold excess crust under and press together to form thick crust edge; flute. Prick bottom and side with fork.
Bake 10 to 12 minutes or until light brown. Cool completely.
In medium bowl, beat pudding mix and milk with whisk 2 minutes. Refrigerate while crust is cooling.
When crust is cool, stir white vanilla baking chips into pudding. Spread pudding into cooled crust. Place piece of plastic wrap over top of pie, touching surface of pudding. Refrigerate at least 4 hours until pudding is completely set.
Spread whipped topping over pudding. Sprinkle miniature semisweet chocolate chips on top of pie.