Preheat the oven to 350°.
In a large mixing bowl, cream the butter and peanut butter together until well blended.
Add the white sugar and brown sugar and beat together with an electric mixer for 2-3 minutes. Add the egg and vanilla and continue to beat together for 2-3 more minutes.
Add all of the dry ingredients and mix just until combined. Stir in the chocolate chips.
Place the mixture in a greased 8X8 pan and press until evenly distributed and flat on the top. Bake for 20 minutes and then allow to cool. Prepare the peanut butter frosting and spread on top of the cooled brownies.