In a small bowl, mix all the marinade ingredients (lime zest, lime juice from 2 limes, 2 cloves minced garlic, salt, and pepper).
Wash and pat dry chicken thighs.
Put the meat and marinade in a Ziploc bag and refrigerate for 30 min- 12 hours.
When the ready to cook, preheat the oven to 350°F.
Take the meat out of the Ziploc, but reserve the marinade.
Heat 1 tbsp 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.
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 or a lid.
Bake it covered with foil or lid for 35 minutes, then take the lid off and cook uncovered for another 10 minutes (total of 45 minutes) until the rice is fully cooked and the liquid is absorbed.
Take out of the oven, garnish with chopped parsley and serve.