Preheat your oven to 350°F (175°C) and grease a 9x13 inch baking pan.
In a large mixing bowl, combine the melted butter, granulated sugar, and brown sugar. Mix until well combined.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In another bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour half of the brownie batter into the prepared baking pan, spreading it evenly.
Drop spoonfuls of peanut butter over the brownie layer, then pour the remaining brownie batter on top.
Use a knife to swirl the peanut butter into the brownie batter for a marbled effect.
Sprinkle the chocolate chips on top.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow the brownies to cool in the pan before cutting into squares.