Preheat oven to 350 degrees F. Spray an 8×8″ baking pan with nonstick spray or use Golden Barrel coconut oil to coat pan evenly. Set aside.
In separate medium-sized bowl, measure out flour, baking powder, and salt. Set aside.
In a bowl attached to a stand mixer (or with a hand mixer), cream butter and peanut butter until smooth. Add sugars and mix well for several minutes. Add eggs, one at a time, and vanilla extract and beat for about 2 minutes.
With mixer on low speed, add in dry ingredients and mix until just combined. Spread batter into prepared pan. Sprinkle chocolate chips on top of batter evenly.
Bake for 5 minutes then remove pan from oven and run a knife through the chocolate to make swirls. Stick pan back in oven and bake for an additional 15-20 minutes, making sure to not overbake. Take bars out when outer edges are slightly browned. Let cool on rack for at least 10 minutes before cutting into bars.