In a large re-sealable plastic bag, or in a large bowl, combine all of the ingredients for the Lime Marinade.
Place the chicken thighs in with the marinade and make sure they are all well covered. Seal the bag, or cover the bowl with a lid. Place in the refrigerator to marinade for at least 30 minutes, or up to 8 hours.
When ready to cook, preheat the oven to 350F with a rack in the middle position. To cook this recipe you will need a large oven-proof casserole skillet which has a lid.
When ready to cook, preheat the oven to 350F and place the skillet on the stove over medium-high heat. Drizzle a little bit of olive oil in the pan and place the the chicken thighs, one at a time, skin side down. Discard the remaining marinating liquids.
Cook the Thighs 5-8 minutes per side, or until they get a nice golden color on each side. Remove from the pan onto a clean plate and reserve.
In the same skillet on medium-high heat, cook the prepared onion and bell pepper pieces and sprinkle in the salt. Cook for 5 minutes.
Deglaze the pan by slowly pouring in the broth. Use your spoon or spatula to scrape off any stuck on bits from the bottom. Bring to a simmer.
Stir in the Dijon mustard and ¼ cup of the chopped cilantro into the broth. Evenly place the rice into the broth. You want to make sure the rice is level in the pan for even cooking.
Place the seared chicken thighs on top of the uncooked rice in the skillet. They should be skin side up. Place the lid on the skillet and place in the preheat oven.
Cook the covered dish in the oven for 20 minutes. After that time, remove the lid and continue cooking for 10 minutes. The chicken is ready when the internal temperature reached 165F. Remove from the oven.
Serve hot with the rest of the chopped fresh cilantro and extra lime wedges.