Peel yams and cut into small pieces. Bring to a boil on stovetop and let simmer 20 minutes or until soft. Mash with a hand mixer or hand masher and set aside.
Pre-heat oven to 350 degrees. Heat olive oil in frying pan. Add onion and saute about 3 minutes. Add ground chicken and garlic. Once chicken is almost cooked through, add mushrooms, carrots, celery and saute until the chicken is fully cooked. In a deep baking dish, layer the chicken mixture on the bottom, cover with a thin layer of mashed yams, then another layer of chicken and top with the remaining yams. Bake for about 20 minutes, then broil for 5 minutes. Let cool 5 to 10 minutes and serve.