In an 8 quart stock pot, over medium heat, melt butter. Add chopped onion, celery, and fennel. Sprinkle with salt and ground pepper. Saute, about 10 minutes, until vegetables are softened.
Add chopped chestnuts, apples, thyme, chicken broth, and water. Increase heat until boiling, then reduce to simmer, covered for 45 minutes.
Use an immersion blender to puree soup or work in small batches using a blender or food processor.
If too thick, add additional water. Adjust seasonings with salt and pepper. Stir in Pernod or Pastis, if using. Sour cream can be stirred in or diluted a bit with water and drizzled over individual bowls when serving. Garnish with fennel fronds.