Place the chicken thighs in the bottom of the slow cooker. Add the chopped onion, sliced bell peppers, and sliced carrots on top.
In a small bowl, stir together the minced garlic, grated ginger, chicken broth, Thai red curry paste, and fish sauce until the curry paste is mostly dissolved.
Pour the broth mixture over the chicken and vegetables in the slow cooker. 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. Cook on low for 15 more minutes until heated through.
Ladle the soup into bowls and top each serving with chopped cilantro.