Add the chicken thighs to the slow cooker. Pour in the coconut milk and stir in the red curry paste until the paste is mostly dissolved.
Add the onion, red bell pepper, carrots, garlic, ginger, fish sauce, and brown sugar. Stir everything together so the chicken and vegetables are coated.
Cover and cook on low for 6 to 7 hours until the chicken is very tender.
Stir in the lime juice right before serving to brighten the sauce.
Spoon the curry over bowls of cooked jasmine rice and sprinkle with the chopped cilantro.