Heat 2 tablespoons of olive oil in a large skillet or Dutch oven over medium-high heat.
Season chicken thighs with salt and pepper. Brown the chicken skin-side down for about 5-6 minutes, then flip and cook for another 3-4 minutes. Remove and set aside.
Add the remaining 1 tablespoon of olive oil to the same pan. Sauté the onion, bell pepper, and celery for 4-5 minutes until softened.
Stir in the garlic, smoked paprika, thyme, and flour. Cook for another 1-2 minutes.
Gradually whisk in the chicken broth and bring to a simmer, scraping up any browned bits from the pan.
Add the uncooked rice and stir to combine.
Nestle the browned chicken thighs on top of the rice mixture. Cover with a lid and reduce heat to low.
Simmer for 35–40 minutes or until rice is tender and chicken is fully cooked (internal temp should reach 165°F).
Garnish with chopped parsley if desired and serve hot.