Sprinkle the chicken with 1/2 tsp salt and 1/4 tsp pepper. Place the chicken, skin side up, in a lightly greased 13x9x2 inch pan. Add 1/3 cup water to the pan. Dot the chicken with butter. Bake, uncovered, at 350 degrees for 40 minutes.
Bring 8 cups water to a boil; stir in orzo and oil. Reduce heat to medium, and cook 8 minutes. Drain well and set aside.
Remove the chicken, reserving the drippings in the pan. Set the chicken aside, and keep it warm.
Add 1 cup water and chicken broth to the drippings; stir well. Add the orzo, tomato paste, 1 tsp salt, and 1/4 tsp pepper, stirring well. Place the chicken on top of the orzo mixture. Bake, uncovered, for 40 additional minutes or until all the liquid is absorbed. Sprinkle with the cheese. Top with yogurt if desired.