Preheat oven to 400 degrees F. Grease a 9x13 pan or similar size 3-quart baking dish with cooking spray and set aside.
Make the onions: Melt butter in a very large skillet over medium high heat. Add the sliced onions and cook for 5-7 minutes, until softened. Season lightly with salt and pepper, reduce the heat to medium and cook for 15 more minutes, until caramelized. (If pan dries out, add ¼ cup of chicken broth to deglaze.)
Season the chicken lightly with salt and pepper and with the oregano and garlic powder. Place in the prepared baking dish.
Mix together the sour cream, cheddar cheese and cream of chicken soup until well combined.
Add the caramelized onions on top of the chicken in the baking dish. Dollop the creamy mixture on top of the onions and spread into a somewhat even layer. Top with the additional Swiss/Gruyere/mozzarella cheese, if using.
Bake at 400 for 40-45 minutes, or until the chicken is cooked through to an internal temp of 165 degrees F. (If you are using large chicken breasts, your cook time will be longer.)
Top with the French fried onions and bake for 3-5 more minutes (watch so they don’t burn). Serve hot.