Make and bake brownies according to the directions on the box, substituting 1/4 cup dark rum for the 1/4 cup water.
Let brownies cool slightly in the pan.
Microwave the chocolate chips in a glass bowl for 30 seconds. Mix with a spoon, then microwave 30 more seconds if needed.
Warm the heavy cream in a saucepan until slightly warm. Add the rum and the chocolate chips and stir until smooth.
Cut the brownies and transfer to a plate. Drizzle the warm sauce on the brownies and serve.