Add the shredded chicken, onions, peppers, garlic, ginger, mushrooms, and brown sugar to a 6-quart slow cooker.
Pour in the broth, coconut milk, Thai curry paste, soy sauce, and rice wine vinegar, then give everything a good stir until combined.
Cover with the lid and cook on HIGH for 2½ hours or on LOW for 4 hours, stirring occasionally.
Stir in the lime juice and adjust the seasoning to taste. Ladle the soup into bowls and finish with sliced green onions, fresh cilantro, and a lime wedge. Enjoy!
