While you can serve anything you like with Chicken Cordon Bleu, I like to keep the side dishes simple and light because of the richness of the Chicken Cordon Bleu. Some of my favorite vegetables to serve with it are steamed broccoli with a light lemon butter sauce, roasted asparagus, or a simple side salad. Chicken Cordon Bleu goes well with mashed potatoes or a simple rice pilaf, like this recipe for homemade herb rice-a-roni.