Do not use low-fat peanut butter; the cookies will not turn out correctly. I use Jif (all are gluten free), but it’s my understanding that Peter Pan (all), Planters (Creamy and Crunchy), Reeses, and Skippy (Creamy, Crunchy, Super Crunchy, Roasted Honey Nut) are also gluten free. One reader/tester successfully made these using all natural peanut butter, but advises that you must press them down a bit before baking---with a fork or the bottom of glass will work---for them to spread enough. You can easily substitute other nut and seed butters in this recipe. We love them made with almond butter. Ensure your vanilla and chocolate chips are GF. I make my own vanilla, but most are gluten free (e.g., McCormick's).
From the celiac listserv (originator unknown)