Cut chicken into 1-inch pieces. Place chicken in a 4- to 5-quart slow cooker and combine with cauliflower, carrots, onions, bamboo shoots, lemongrass, ginger, garlic, and crushed red pepper. Pour chicken broth over mixture in cooker.
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 coconut milk, snow peas, serrano peppers, and lime peel. Cover and let stand for 15 minutes.