Melt the butter in a large saucepan over low heat. Add the marshmallows and stir until completely melted. Remove from heat.
Off the heat, add the peanut butter and stir until completely melted and smooth. Add the Rice Krispies cereal, pretzel pieces and peanut butter chips, stirring gently until all dry ingredients are coated. Turn the mixture into the prepared baking dish and press it into the pan, creating an even top.
Microwave the chocolate chips on 50% power in 30-second intervals, stirring after each, until completely melted and smooth. Pour the chocolate over the treats and spread in an even layer with an offset spatula. Let cool at room temperature until set, about 1 hour. (You can also refrigerate the treats for about 30 minutes to speed up the process.) Store leftovers at room temperature in an airtight container.