Preserved lemons pack a tart and salty punch to any dish. They are made by rubbing cut lemons with salt, pressing them tightly in a jar with aromatics, and letting them “pickle” for a couple of weeks. Look for them in the grocery store in the same aisle as pickles and condiments.
Preheat the broiler. Cook the rice as the label directs. Meanwhile, heat the olive oil in a large ovenproof skillet over medium-high heat. Season the chicken with salt and pepper. Add to the skillet, skin-side down, and cook until golden, 6 to 8 minutes. Flip and cook until just browned on the other side, about 3 more minutes.
Transfer the chicken to a plate and pour off the excess fat from the skillet. Return the skillet to medium-high heat and add the butter; let melt. Add the bell pepper and onion and cook until just softened, about 4 minutes. Add the garlic and 1/2 teaspoon each salt and pepper and cook 1 more minute. Add the wine, scraping up any browned bits from the bottom of the pan. Stir in the chicken broth and preserved lemon slices and bring to a simmer.
Return the chicken to the skillet, skin-side up. Simmer until the chicken is cooked through and the liquid is reduced by half, about 10 minutes. Place the skillet under the broiler and cook until the chicken skin is crisp, 2 to 3 minutes.
Fluff the rice and divide among plates. Serve with the chicken, vegetable mixture and sauce from the skillet; top with dill.