1. Heat the oil in a 4-quart saucepan over medium-high heat. Add the carrot and pepper and cook for 5 minutes or until tender-crisp, stirring occasionally. Stir in the mushrooms, if desired.
2. Add the broth to the saucepan and heat to a boil. Reduce the heat to medium-low. Stir in the chicken and cook for 5 minutes or until the chicken is hot, stirring occasionally.
3. Stir in the coconut milk and cook until the mixture is hot and bubbling. Stir in the lime juice and cilantro just before serving.