Line a 9 x 13-inch baking dish with foil or parchment paper, leaving an overhang for handles. Spray with non-stick spray. Set aside.
In a large glass bowl, melt 1/2 cup butter in the microwave. Stir in peanut butter, confectioner's sugar, and graham cracker crumbs. (I prefer to use an electric mixer) The dough will be very stiff. Spread dough in the prepared dish, pressing down evenly.
In a separate bowl, melt remaining 1/2 cup butter and chocolate chips in the microwave for 1 minute. Stir gently until all chips are melted. You may need to microwave the chocolate mixture for an additional 15 to 30 seconds, stirring until the chocolate chips are melted and the mixture is smooth. Spread this mixture over the peanut butter layer. Refrigerate for 30-45 minutes, cut into squares. Store bars in the refrigerator.