Melt the butter over medium heat in a large soup pot. Add the carrots, onions, leeks, and celery, 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 chicken 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 and a drizzle of olive oil, if desired.