Season the chicken thighs on both sides with kosher salt and black pepper.
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 the other side for 3 minutes. Remove chicken from the skillet and set aside.
Reduce heat to medium. Add sliced onion to the skillet and cook, stirring occasionally, until softened and lightly caramelized, about 8 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to form a roux.
Slowly pour in the chicken broth while stirring to avoid lumps.
Add smoked paprika, dried thyme, and dried oregano. Stir to combine and bring the mixture to a simmer.
Add the rinsed rice to the skillet and stir to evenly distribute.
Nestle the browned chicken thighs skin-side up into the rice mixture.
Cover the skillet with a tight-fitting lid, reduce heat to low, and cook for 25-30 minutes until the rice is tender and the chicken is cooked through (internal temperature 165°F).
Remove the lid and carefully transfer the chicken to a plate.
Stir the unsalted butter into the rice mixture until melted and creamy.
Return the chicken to the skillet, spoon some sauce over the top, and sprinkle with chopped fresh parsley before serving.