Dirty rice is jambalaya’s less complex brother, yet in its way, it’s every bit as delicious. Unlike jambalaya, which can be served as a main course, dirty rice is a side dish. It’s also a way to use all the stuff you pull out of the cavity of a whole chicken. While you can use the heart, I usually leave it out because it’s tough, even chopped up. If the liver component of the giblets is about 50 percent, that’s perfect.