Preheat oven to 350 degrees F (180 degrees C). Mix flour, baking soda and salt; set aside.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the egg, then stir in the vanilla. Mix in the dry ingredients until well blended. Stir in the chocolate chips and walnuts. Roll the dough into 2 inch balls and place them 3 inches apart onto ungreased cookie sheets.
Bake for 20 to 23 minutes in the preheated oven. Allow cookies to cool for a few minutes on the baking sheet before removing to a wire rack to cool completely.
