Bring a large pot of salted water over high heat for the egg noodles. Discard the skin from the chicken and remove the meat from the bones. Shred the chicken meat with your fingers or two forks and reserve.
Place a large skillet over medium-high heat with the EVOO. Add the onion, carrot and celery to the pan, and cook until the veggies begin to get tender, 3-4 minutes. Toss the zucchini into the pan along with some salt and freshly ground black pepper, and cook another 2-3 minutes until all the veggies are tender.