Heat coconut oil in a large saucepan over medium heat. Add chicken and sear for 1 minute per side. Add 1 can chicken broth. Bring to a simmer and cook until chicken is no longer pink in the center and the juices run clear, 20 to 25 minutes.

Remove chicken with a slotted spoon, leaving the cooking broth in the saucepan. Add the remaining can of chicken broth, sweet potatoes, onions, carrots, apple, celery, cilantro, garlic, curry powder, salt, and pepper. Add water to cover. Bring to a boil and cook until sweet potato is tender, 10 to 12 minutes. Cool slightly.

Meanwhile, when chicken is cool enough to handle, dice and set aside.

Fill blender halfway with cooked vegetable and broth mixture. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour into a separate saucepan. Puree remaining vegetables and broth.

Add diced chicken and coconut milk to the pureed vegetable mixture. Reheat over medium heat, 5 to 10 minutes.