Preheat the oven to 350 degrees F (175 degrees C).
In a large bowl, cream together the butter, oil, brown sugar, and white sugar until smooth. Beat in the eggs and vanilla. Combine the flour, baking soda, cream of tartar, and salt; stir into the creamed mixture. Mix in the chocolate chips and walnuts. Drop dough by rounded teaspoons onto ungreased cookie sheets.
Bake for 12 to 15 minutes in the preheated oven, or until light brown. Allow cookies to cool on the baking sheets for a couple of minutes before transferring to wire racks to cool completely.