In a small bowl, whisk together the peanut butter, coconut milk, chicken broth, soy sauce, rice vinegar, honey, and garlic. If the sauce is difficult to stir, pop it in the microwave to slightly melt the peanut butter.
Cook on low for about 4 hours. During the last thirty minutes of cooking, open up the slow cooker and add the red peppers. When finished, shred the chicken and add back to the slow cooker. Give it a good stir so it can soak up the sauce. Let it hang out in the sauce for 10-15 minutes. Serve with fresh lime juice and cilantro.