Heat a large pot or Dutch oven over medium heat. Add the coconut oil and the onion. Cook until soft and add the garlic. Cook for 1 more minute and add the cauliflower and curry powder. Stir and cook for 1 more minute. Season with salt and pepper.
Add the chicken stock and chicken breasts. Bring to a boil and reduce to simmer. Simmer for 20 minutes, until cauliflower is tender and chicken is cooked through.
Remove chicken breasts from pot, shred with two forks and return back to the pot. Add the coconut milk, cilantro, and lime juice. Stir and simmer about 5-10 minutes, until heated through.