Add the chicken thighs to the slow cooker. Spoon in the red curry paste, half the coconut milk, sliced bell pepper, sliced onion, fish sauce, and brown sugar. Stir everything so the chicken is coated.
Cover and cook on low for 6 to 7 hours until the chicken is very tender.
About 20 minutes before the chicken is done, combine the jasmine rice, remaining coconut milk, and water in a small saucepan. Bring to a boil, then reduce heat, cover, and simmer until the rice is cooked and creamy.
Shred or slice the chicken in the slow cooker and stir it back into the sauce. Serve the curry over the coconut rice with cilantro and lime wedges on top.