Place the chicken thighs in the bottom of the slow cooker.
Add the chopped onion, sliced carrots, sliced red bell pepper, minced garlic, and grated ginger around the chicken.
In a bowl, whisk together the coconut milk, chicken broth, red curry paste, fish sauce, and brown sugar until smooth.
Pour the mixture over the chicken and vegetables in the slow cooker.
Cover and cook on low for 6 hours until the chicken is tender.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
Stir in the lime juice right before serving.
Ladle into bowls and top with fresh cilantro.