Whisk together to combine thoroughly the brown rice flour, potato starch, and tapioca flour.
Measure 2 ¼ cups plus 2 tablespoons of this mixture (12 ¾ ounces) and transfer it to another bowl.
Whisk in the xanthan gum, salt, and baking soda. You’ll have a few tablespoons of leftover mix. Save it to flour foods you’ll be frying or for a sauce you’ll thicken.
Melt the butter and transfer it to the bowl of a stand mixer.
Add both sugars, attach the flat beater, and beat on medium low speed until smooth and the butter is incorporated into the sugars, about 1 minute. You shouldn’t see any butter floating around by itself.
Add the eggs and vanilla and beat on medium speed until creamy, about 1 minute.
While beating on low, gradually add the flour mixture and beat until thoroughly combined.
Scrape the bowl and beater and stir in the chocolate chips with a wooden spoon.
Cover tightly and refrigerate overnight or for up to 3 days.
To bake, adjust an oven rack to the center position and preheat the oven to 375 degrees.
Divide the dough into 24 portions, 2 ounces each.
Roll each into a ball. The ball of dough will measure about 1 3/4-inches in diameter.