Saute the carrots, onions, leeks, and celery in a large pot and cook until tender but not browned, about 10 minutes. Stir in the thyme and mushrooms and cook for 5 minutes, until the mushrooms have softened. Add the stock, salt and pepper, and simmer, covered, for 30 minutes.
Puree the soup in a food processor or blender in as many batches as necessary. Adjust seasoning to taste.
Serve in warm bowls with a sprinkling of chives.