Melt the butter in a medium saucepan. Add the carrot, celery, and onion, and cook over medium-low heat, stirring, until softened, about 10 minutes. Add the chestnuts and cook for 4 minutes. Add the port and thyme; cook over medium-high heat until the port is reduced by half, about 4 minutes. Add the stock and bring to a boil. Cover partially and simmer over low heat for 30 minutes. Remove and discard the thyme sprig.

Add the cream to the soup. Working in batches, pour the soup into a blender. Secure lid on blender and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth. Return the soup to the saucepan. Bring soup to a simmer. Season with salt and pepper and serve.