The phrase "to serve with the chicken" typically refers to a dish or side item that is served alongside roasted, grilled, or baked chicken. Full definition
Let cook for a few minutes and then serve with the chicken soup out of the crockpot. (heathersbytes.com)
Traditionally you would save, not serve, the broth — it improves each time you use it — but we can never resist serving it with the chicken as a light sauce. (foodandwine.com)