Generously season the chicken thighs with salt & pepper.
Heat the oil in a dutch oven or large pot over medium-high heat. When the oil is hot sear the chicken thighs skin-down down until skin is browned, about 5 minutes. Transfer chicken to a plate and set aside.
Keep the heat at medium-high and add the onion, garlic, celery, and carrots. Cook, stirring occasionally, for about 1 minute.
Stir in the water, rosemary, rice, and 1 tsp salt. Return the chicken thighs to the pot and bring to a boil.
Cover the pot and reduce the heat to medium-low. Simmer for about 45 minutes or until chicken is very tender.
Transfer the chicken to a plate then shred the chicken discarding the skin and bones.
Stir the shredded chicken back into the pot then taste the soup and season with additional salt & pepper if needed.