Cover cookie sheet with waxed paper. Heat chocolate chips, corn syrup, peanut butter, milk and vanilla in 3-quart saucepan over medium heat, stirring constantly, until chocolate is melted and mixture is smooth; remove from heat. Stir in oats and peanuts until well coated.
Drop mixture by rounded tablespoonfuls onto waxed paper. Refrigerate uncovered about 1 hour or until firm. Store covered in refrigerator.