Stir together butter, sugars until creamy. Beat in vanilla and egg until blended.
Stir in flour mixture until blended. Stir in chocolate chips and nuts. Put in the refrigerator and let chill for 2 hours. Preheat oven to 375°F Drop batter by tablespoonfuls onto baking sheets covered with parchment paper.
Bake for 12 minutes or until golden brown. Cool on sheets for 5 minutes and transfer to racks to cool completely.