Place chicken thighs in the bottom of the slow cooker. Add diced onion, garlic, chopped carrots, and celery.
Pour in the uncooked rice and chicken broth. Add salt, pepper, and olive oil. Lightly stir to combine, making sure chicken is mostly covered.
Cover and cook on LOW for 5–6 hours or HIGH for 2.5–3.5 hours, until chicken is tender and rice is cooked through.
Shred chicken with two forks directly in the pot. Stir everything together until creamy. If using, mix in shredded cheese now.
Taste and adjust seasoning. Top with chopped parsley or green onions before serving.