In a medium saucepan combine wild rice, water and 1/4 teaspoon salt. Bring to boiling; reduce heat. Simmer, covered, about 40 minutes until tender. Drain if needed.
Meanwhile, in a Dutch oven melt butter over medium heat. Add onion, celery, and carrot; cook 5 minutes or until soft, stirring occasionally. Add mushrooms and garlic; cook 5 minutes or until vegetables are tender and most of the mushroom liquid evaporates, stirring frequently. Carefully add wine; cook and stir 1 minute.
Add broth, chicken, the 1/2 teaspoon salt, and the pepper. Bring to boiling; reduce heat. Simmer, uncovered, 10 minutes.
In a small bowl stir together cream and flour; add to soup mixture. Cook and stir until slightly thickened and bubbly. Stir in cooked wild rice and thyme. Return to boiling; reduce heat. Simmer 5 minutes to blend flavors. Season to taste with additional salt and black pepper.