Preheat your oven to 360 degrees F and prepare a 9-inch x 13-inch baking pan with parchment paper.
In a large mixing bowl, stir together the flour, baking soda, and salt. Set aside.
In a medium mixing bowl, stir together the melted butter, brown sugar, sugar, and vanilla until combined. Stir in the egg and the peanut butter.
Add the peanut butter mixture to the dry ingredients. Gently fold until everything just start to come together.
Add almost all of the chocolate chips and fold them into the cookie dough. Save the extras for the next step.
Transfer the cookie dough into the prepared baking dish and press into an even layer. (see note) Sprinkle the reserved chocolate chips over the top of the dough.
Bake on the middle oven rack for 17-20 minutes. The bars are done when a toothpick inserted in the center comes out mostly clean. (see note)
Let the bars cool for 5 minutes in the pan. Then use the parchment paper to lift them from the pan and transfer them to a wire rack to cool completely. Cut into 15 bars and serve.
Notes
Organic peanut butter is not recommended as it might get too oily for this recipe.
Baking time depends on your oven, the pan you use, and how chewy you want the bars to be. Check them after around 15 minutes of baking.
I used a 9-inch x 13-inch pan, if you want them to be thicker, use an 8-inch x 8-inch pan and bake them 3-5 minutes longer.