Place the sliced onion, minced garlic, and grated ginger in the bottom of the slow cooker.
Add the chicken breasts on top of the aromatics.
In a bowl, whisk together the coconut milk, red curry paste, fish sauce, and brown sugar until smooth.
Pour the coconut mixture over the chicken and add the sliced red bell pepper.
Cover and cook on low for 5 to 6 hours until the chicken reaches an internal temperature of 165°F.
While the chicken cooks, bring the water to a boil in a medium pot. Add the jasmine rice, reduce to a simmer, cover, and cook for 15 minutes. Remove from heat and let it rest covered for 5 minutes.
Shred or slice the chicken in the slow cooker and stir in the lime juice.
Spoon the chicken and sauce over the cooked jasmine rice. Sprinkle with chopped cilantro before serving.