The Palmer House Brownie described by Wikipedia uses walnuts.
The dessert is part of the Palmer House Hotel’s origin story for the brownie. Its reported formula combines chocolate with walnuts and an apricot glaze, producing a richer and more elaborate confection than many modern home-style brownies.
Walnuts are not essential to every brownie. Brownie recipes vary widely: some use pecans, almonds, or hazelnuts, while others omit nuts entirely. That variation makes the question specifically about the Palmer House version important. The answer refers to the named historical preparation, not brownies in general.
The Palmer House account dates the request to 1893, when Bertha Palmer wanted a portable dessert for visitors to the World’s Columbian Exposition. The hotel has continued serving a version associated with the original recipe, helping preserve the walnut-and-apricot identity of this particular brownie.