In a large skillet brown chicken pieces, half at a time, in hot oil. Drain off fat. In a 3-1/2- to 5-quart slow cooker place chicken pieces, turkey sausage, and onion. Sprinkle with garlic, dried thyme (if using), black pepper, and saffron. Pour broth and water over all.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3-1/2 to 4 hours. Stir in the tomatoes, sweet peppers, peas, and, if using, the fresh thyme. Cover; let stand for 5 minutes. If desired, serve over hot cooked rice. Makes 6 servings.