Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Toss the chicken with the paprika, 1 teaspoon salt, and pepper in a large bowl. Place the chicken skin-side down in the skillet and cook until golden, 4 to 5 minutes. Remove the chicken to a plate and add the remaining oil.

Add the carrots, celery, and shallots to the skillet and cook until softened, 4 to 5 minutes. Stir in the garlic, thyme, oregano, lemon zest, lemon juice, 1/2 teaspoon salt, and pepper, cooking for another minute. Stir in the rice and cook undisturbed for 2 minutes. Pour in the stock, add 1/2 teaspoon salt, stir, add the chicken back skin-side up, cover, reduce heat, and simmer until rice is tender and chicken is cooked, 15 to 20 minutes. Preheat the broiler.

Remove the lid and broil until the chicken skin is crispy, 2 to 3 minutes. Sprinkle with chives.