Cook chicken in a large skillet, half at a time, in hot oil over medium-high heat until brown on both sides. Drain off fat.
In a 4- to 5-quart slow cooker combine water chestnuts, mushrooms, celery, carrot, onion, and garlic. Top with chicken. Lightly sprinkle with pepper. Combine in a small bowl chicken broth, soy sauce, and ginger. Pour over mixture in slow cooker.
Cover and cook on low heat setting for 5 to 6 hours or on high heat setting for 2 1/2 to 3 hours. Remove chicken to a serving platter, reserving vegetable mixture in cooker. Cover chicken with foil to keep warm.
If using low heat setting, turn to high heat setting. Combine in a small bowl cornstarch and water. Stir into vegetable mixture in cooker. Stir in snow peas. Cover and cook for 15 minutes or until thickened.
Spoon vegetable mixture over chicken. Sprinkle with almonds.