PREHEAT oven to 350º F.
COMBINE flour, cocoa, baking powder and baking soda in small bowl. Beat butter, brown sugar, granulated sugar, oil and egg in large mixer bowl until creamy. Gradually beat in flour mixture. Stir in nuts. Drop by rounded tablespoon onto ungreased baking sheets.
BAKE for 9 to 10 minutes or until edges are set but centers are still soft. Cool on baking sheets for 3 minutes; remove to wire racks to cool completely.