Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together peanut butter, butter, brown sugar, and white sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Stir in flour, baking soda, and salt until just mixed, then fold in melted chocolate chips and peanut butter chips. Cover and chill the dough in the refrigerator for 1 hour.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them 2 inches apart.
Bake for 10-12 minutes or until edges are golden; let cool on the sheet for 5 minutes before transferring to a wire rack.