Combine the melted butter, graham cracker crumbs, powdered sugar, and 1 cup of peanut butter in a large bowl until smooth. Spread the peanut butter mixture evenly in a greased 9 x 13 x 1-inch pan.
Add the remaining ¼ cup of peanut butter and chocolate chips to a medium bowl and heat in the microwave in 30-second increments, stirring between each increment until fully melted. Spread evenly over the top of the peanut butter mixture.
Chill in the refrigerator for at least an hour before serving so that the bars can set. Store leftover bars in the fridge in an airtight container for up to a week.