In a 5 to 6 quart slow cooker combine mushrooms, carrots, onions, and sweet pepper. Add chicken. Pour chicken broth over mixture in cooker. Sprinkle with black pepper.
Cover and cook on low-heat setting for 5 to 6 hours or on high-heat setting for 2 1/2 to 3 hours.
If using low-heat setting, switch to high-heat setting. Combine in a bowl undrained tomatoes, tomato paste and cornstarch. Stir into mixture in cooker. Cover and cook for 20 minutes more or until thickened. Serve with hot cooked rice (optional).