Preheat oven to 375 degrees. In a medium mixing bowl stir together flour, baking soda, and salt. Set aside.
In a large mixing bowl with an electric mixer on medium speed cream butter and sugars until fluffy. Beat in eggs, one at a time, then vanilla. On low speed gradually add flour mixture and mix just until blended. Stir in chocolate chips and walnuts.
Drop dough by rounded tablespoonfuls 2 inches apart on ungreased baking sheets. Bake for 9 to 12 minutes. Transfer cookies to cooling racks to cool.