Preheat oven to 350 degrees. Trim any excess fat from the chicken pieces and season with salt and pepper. Place the chicken pieces, skin side up in a shallow baking pan. Place into the pre-heated oven and cook for 15 minutes.
While chicken is in the oven, make the sauce by combining the melted butter, garlic, olive oil and lemon juice in a small bowl.
Remove chicken from oven and pour off any grease. Put the chicken back into the baking pan, skin side down this time. Pour the sauce over the chicken and add the shallots and lemon rinds to the pan. Return to the oven and continue cooking for another 12 minutes.
Remove the pan from the oven and flip the chicken pieces over, skin side up. Return to the oven and bake until golden brown, with an internal temperature of 165 degrees. While chicken is finishing, boil as many servings as you need of orzo pasta. Be sure not to over cook it.
When the chicken is done, remove the pan from the oven and take the chicken pieces out to rest on a plate. Add the cooked pasta to the pan with the juices and return to the oven and cook until heated through. Pour the pasta and sauce onto a serving platter, place chicken pieces on top and serve hot.