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