Although this can vary by personal taste, a typical side dish to serve with chicken Parmesan is pasta with marinara sauce. Spaghetti noodles are the most commonly used pasta, but penne or angel hair pasta are popular as well.
It is also common to serve a salad and garlic bread with the meal. The salad can be a regular house salad or a Caesar salad. Steamed or sauteed vegetables like broccoli or Brussel sprouts are a good substitute for salad during colder months. The garlic bread will vary based on preference, but a good choice is regular French bread with a garlic spread heated until toasted.