Cook the chicken: Season the chicken breasts with salt and pepper on both sides. Heat the oil in a large skillet over medium-high heat. Brown the chicken on both sides, then reduce the heat to medium and cover the skillet with a lid. Checking from time to time, cook the chicken until it’s done all the way to the center and juices run clear. Depending on the thickness and size of your chicken breast, this will take 10-15 minutes, or more for very large pieces. Remove the chicken from the skillet and cover on a plate.
Cook the pasta and asparagus: Add the pasta, broth, milk and garlic powder to the skillet. Season with salt and pepper and stir well. Bring to a boil, then reduce the heat and simmer for 5 minutes (do not cover with a lid). Add the sliced asparagus and finish cooking until the pasta and asparagus are done and the sauce has thickened.
Finish the dish: Stir the parmesan and lemon zest into the pasta. Slice the chicken breast and serve immediately over the pasta.