In a small bowl, mix all the marinade ingredients (lime zest, lime juice, minced garlic, salt, and pepper).
Wash and pat dry chicken thighs.
Put chicken and marinade in a Ziploc bag and refrigerate for 30 min- 1 hour.
When the chicken is ready, preheat the oven to 350°F.
Take the chicken out of the Ziploc, but reserve the marinade.
Heat a tablespoon of olive oil in a heavy skillet over medium/high heat. Brown the chicken from both sides, starting with the skin down. Then remove to a plate and set aside.
Wipe the skillet with a paper towel from the excess fat and burnt bits.
Add rice, the reserved marinade, chicken broth, and water to the skillet. Season with salt and pepper and stir.
Place the chicken on top of the rice and cover with foil.
Bake it covered with the foil for 35 minutes, then take the foil out and cook for another 10 minutes (total of 45 minutes) until the rice is fully cooked and the liquid is absorbed.
Take it out of the oven, garnish with chopped parsley and serve.