Prepare wild rice according to package directions to desired doneness; drain.
Meanwhile, in large saucepan or Dutch oven, heat oil over medium heat. Add mushrooms, onions, carrots, garlic and thyme; salt and pepper to taste. Sauté until carrots are softened (about 5-7 minutes).
Stir in flour; cook 1 minute. Add sherry or ¼ cup chicken broth. Stir in chicken broth, chicken and wild rice. Bring to a boil; simmer 5 minutes. Stir in half & half; continue cooking until heated through.