Season the chicken thighs with salt and black pepper on both sides.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken thighs skin-side down and cook for 5-7 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove chicken from the pot and set aside.
Reduce heat to medium. Add diced onion, carrot, and celery to the pot and sauté for 4-5 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice, dried thyme, smoked paprika, and ground turmeric. Cook for 1-2 minutes to toast the rice slightly.
Pour in the chicken broth and stir to combine, scraping any browned bits from the bottom of the pot.
Return the chicken thighs to the pot, placing them on top of the rice mixture skin-side up.
Bring the liquid to a simmer, then reduce heat to low. Cover the pot with a tight-fitting lid and cook for 25 minutes without lifting the lid.
After 25 minutes, check that the rice is tender and the chicken is cooked through (internal temperature should reach 165°F or 74°C). If needed, cook uncovered for an additional 5 minutes to evaporate excess liquid.
Remove the pot from heat and let it rest, covered, for 5 minutes.
Sprinkle chopped fresh parsley over the dish before serving.