Melt the margarine in a large, deep ovenproof saute pan or stove-top casserole dish over medium heat. Add the squash, onion, green pepper, mushrooms, tomatoes, oregano, parsley, poultry seasoning, and black pepper.
Bring to a boil over high heat. Reduce heat to low, cover, and simmer until the vegetables are tender, approximately 10 minutes.
Arrange the chicken on top of the vegetables. Sprinkle with the Parmesan and paprika. Cover and bake until an instant-read thermometer registers 160 degrees F in a breast and the juices run clear, 25 to 30 minutes.
Turn on the broiler and broil until the top is nicely browned, about 5 minutes.