Heat 1 tablespoon of the oil in the dutch oven over medium-high heat. Toss the chicken with the paprika, 1 teaspoon salt and a few grinds of pepper in a large bowl. Place the chicken skin-side down in the skillet and cook undisturbed until the skin is browned, 4 to 5 minutes. Flip it over and brown the other side for another 3-4 minutes. Remove the chicken to a bowl and add the remaining 1 tablespoon oil to the skillet.
Add the onions stirring to scrape up all the brown bits from the bottom of the pan. Cook for 3 minutes and then add carrots and celery to the skillet and cook, stirring occasionally, for another 4 to 5 minutes.
Stir in the garlic, thyme, oregano, lemon zest, 1/2 teaspoon salt and a few grinds of pepper and cook just until you begin to smell the garlic, about 1 minute. Stir in the rice and cook undisturbed until lightly toasted, about 2 minutes.
Pour in the broth and stir to combine, then add the chicken thighs back to the pan with all the juices in the bowl, skin-side up. Bring the liquid to a boil then cover, reduce the heat to a simmer and cook until the rice is tender and the chicken is cooked through, 20 to 25 minutes.
Remove the lid from the pan and broil until the chicken skin is crispy and golden, 2 to 3 minutes.