Place the chicken thighs, chicken broth, red curry paste, onion, red bell pepper, carrots, garlic, ginger, fish sauce, and brown sugar into the slow cooker.
Stir gently to combine the curry paste with the broth.
Cover and cook on low for 6 hours.
Remove the chicken thighs, shred them with two forks, and return the meat to the slow cooker.
Stir in the coconut milk and lime juice. Cover and cook on low for 30 more minutes.
Ladle into bowls and top with chopped cilantro before serving.