Heat a large saucepan over medium heat. Add half the oil. Add the carrots, onion, mushrooms and parsley. Saute for about 10 minutes or until onions begin to brown. Add wild rice, walnuts, black pepper and chicken stock. Bring to a boil, then reduce to simmer. Cover and cook for 40 minutes.
In the meantime, add the rest of the oil to a saute pan. Add chicken breasts and brown on both sides, about 3 minutes a side. Cook until internal temperature is 165 F. Remove chicken from pan and set aside, keeping warm.
Add diced beets and squash to the hot saute pan. Saute over medium heat for 15-20 minutes or until squash begins to brown and both squash and beets are tender. Add chopped greens, balsamic vinegar, cranberries and the rice mixture. Toss to combine and loosen cooked bits from bottom of pan.
Divide among four bowls. Top with slices of chicken breast and serve.