Melt the butter, then mix in sugars. Add the vanilla, salt, and baking soda; mix well. Add eggs one at a time. Add half the flour, the chocolate chips, the nuts, and stir well. Add remaining flour and mix thoroughly.
Drop by teaspoons onto a greased cookie sheet. (If dough is too sticky, chill for a while.) Bake at 350 for 10-12 minutes until nicely browned. Let cool on cookie sheet for two minutes, then remove to wire rack to cool completely.