In a medium pot over medium-high heat, saute chicken, onion, garlic, and carrots in olive oil until chicken is no longer pink. Add mushrooms and saute an additional 2 minutes.
Reduce heat to medium and stir in flour until smooth. Slowly stir in chicken broth until smooth. Add half-and-half, cooked wild rice, thyme, and salt and pepper to taste.
Bring soup to a simmer then reduce heat to low and let simmer 15-20 minutes, covered until slightly thickened and vegetables are tender. Serve soup hot and enjoy!