Preheat oven to 350 degrees F. Combine flour, oats, baking powder, baking soda and salt in a medium bowl; set aside. Beat peanut butter and butter in a large bowl with mixer at medium speed until smooth; beat in oil. Beat in brown sugar and sugar until blended, then eggs and vanilla. Stir in flour mixture and chocolate chips, if desired.
Shape dough into 1-inch balls. Place 2 inches apart on ungreased cookie sheets. Flatten with fork dipped in sugar, making crisscross pattern. Bake 10 to 12 minutes or until lightly browned. Remove to cool completely on wire rack. Store in tightly-covered container.
