Preheat the oven to 350 degrees . In a large, deep skillet over medium-high heat, cook the sausage, breaking it into bits with a wooden spoon, until browned, about 10 minutes. Add the onion, celery, carrots and apples and cook over high heat, stirring frequently, until soft, about 10 minutes.
In a large bowl, combine the stuffing mix with the chestnuts, walnuts and sausage mixture. Add the chicken broth and combine thoroughly. Season to taste with salt and pepper.
Spoon the stuffing into 2 buttered 3-quart casserole dishes and bake, covered, for 40 minutes.