Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Season the chicken thighs with salt, black pepper, and smoked paprika on both sides.
Place the chicken thighs skin side down in the hot oil 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 skillet and set aside.
In the same skillet, add diced onion, carrot, and red bell pepper. Cook for 4-5 minutes until vegetables are softened.
Add minced garlic and dried thyme to the vegetables and cook for 1 minute until fragrant.
Add the rice to the skillet and stir to coat it with the oil and vegetables.
Pour in the chicken broth and stir to combine. Bring the mixture to a gentle boil.
Return the chicken thighs to the skillet, placing them on top of the rice mixture, skin side up.
Reduce heat to low, cover the skillet with a tight-fitting lid, and simmer for 25 minutes until the rice is tender and the chicken is cooked through.
Remove the skillet from heat and let it rest, covered, for 5 minutes.
Sprinkle chopped fresh parsley over the dish before serving.