Heat oil in a large pot or Dutch oven over medium heat. Add chicken to the pot and sprinkle salt and pepper on top. Cook until the chicken is cooked throughout, turning the chicken over to cook all sides as it cooks. Then, using a slotted spoon or tongs, transfer the cooked chicken to a plate and set aside. Add diced potatoes, carrots, celery, and onion. Stir vegetables together and sauté until the onions start to look translucent,.