In an ovenproof or cast iron skillet, cook onion in olive oil/butter over medium heat for about 4 minutes or until softened.
Add carrot, celery and chicken broth. Let simmer about 4 minutes until veggies are slightly softened. In a bowl, combine chicken, cream of chicken soup and parsley. Stir into carrot mixture in the skillet.
Cut each biscuit in half and place in skillet on top of chicken mixture. Bake 15 minutes, cover with foil and bake an additional 10 minutes. Serve warm.
Pillsbury Biscuits can be purchased in the refrigerator section of most grocery stores (any variety will work in this recipe). If you cannot find pillsbury biscuits, you can substitute homemade baking powder biscuits in their place.