Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch baking dish.
Stir flour, powdered peanut butter, baking powder, and salt together in a bowl.
Beat peanut butter and butter together in a bowl until creamy. Gradually add white sugar and brown sugar; beat until fluffy. Add eggs and vanilla extract; beat until smooth. Stir in flour mixture and chocolate chips until incorporated into batter. Spread batter into prepared baking dish.
Bake in preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes. Cool on a wire rack.
