Preheat oven to 350°. In a large bowl, cream butter, shortening and sugars until light and fluffy. Beat in eggs and vanilla. Combine flour, salt and baking soda; gradually add to creamed mixture and mix well. Stir in chocolate chips and nuts.
Form dough into 1-1/2-inch balls and place on ungreased baking sheets. Bake until golden brown, 10-13 minutes. Remove from pans to wire racks to cool.