In a very large skillet brown chicken, half at a time, in hot oil. (Add more oil, if necessary.) Set aside.
In a 3-1/2- or 4-quart slow cooker combine onions and carrots. Top with chicken. Sprinkle chicken with salt and pepper. In a small bowl stir together broth, apricot spread, tapioca, mustard, and allspice. Pour over chicken and vegetables in cooker.
Cover and cook on low-heat setting for 8 to 9 hours or on high-heat setting for 4 to 4-1/2 hours. Serve chicken and vegetables with some of the cooking juices. If desired, serve with hot cooked rice. Makes 8 servings.