Heat oven to 450°F Make pie crust as directed on box for One-Crust Baked Shell using 9-inch glass pie pan. Bake 9 to 11 minutes or until light golden brown. Cool.
Meanwhile, in 2-quart saucepan, mix milk and gelatin; let stand 5 minutes. Stir in pudding mix. Cook over medium heat, stirring constantly, until mixture boils. Remove from heat; let stand 5 minutes. Add 3/4 cup vanilla chips to pudding mixture; stir occasionally until melted. Place plastic wrap over surface of pudding; refrigerate 1 hour to cool.
In small bowl with electric mixer, beat whipping cream on high speed until stiff peaks form. Fold 1/3 of whipped cream into cooled pudding mixture. Fold in remaining whipping cream. Spoon pudding mixture into cooled baked pie shell, spreading evenly.
Twist stems of strawberries to remove or use tip of sharp knife, being careful not to cut berries. Place strawberries, pointed ends up, on filling, gently pressing about 1/4 of each berry into filling.
In 1-quart saucepan, heat 3 tablespoons vanilla chips and oil over low heat, stirring constantly, until melted and smooth. Drizzle over strawberries. Refrigerate at least 3 hours or until serving time. Store in refrigerator.