Preheat the oven to 350°F. Grease an 8×8″ square pan and set aside.
In a saucepan over medium heat, melt the butter and brown sugar, stirring constantly until smooth. Remove from the heat, and stir in the peanut butter. Allow to cool.
Meanwhile, combine the flour, baking powder, baking soda and salt in a large mixing bowl.
Add the egg to the butter & sugar mixture and mix well. Add the vanilla extract and stir to combine. Pour the mixture into the prepared dry ingredients, and stir to create a thick, smooth batter. Fold in half the chocolate chips, reserving the rest for sprinkling on top.
Transfer the batter to the prepared pan, spreading the batter evenly to the edges of the pan. Sprinkle with the chocolate chips and lightly press them into the batter.
Bake for 25 minutes until the top is golden and the edges are slightly browned. Allow to cool in the pan. Cut into squares and serve.